Quantum Information and Computation & Condensed Matter Meeting/Seminar

We meet to discuss sciences related to quantum information and quantum computation and condensed matter physics. The meetings take place at CN Yang Institute for Theoretical Physics (6th floor Math Tower).

Fall 2015

See YITP seminar list (shared with theory and pheno groups)

Summer 2015

7/16 Thurs 2:30pm Guanyu Zhu (Northwestern University)

Title: Wonders in flat bands: from quantum liquid crystals to self-correcting quantum memory
Abstract: In this talk, I will discuss two cases where flat bands in frustrated lattice models lead to emergence of interesting physics.

In the first part, I talk about a family of interacting boson models based on a kagome lattice with local synthetic gauge flux, which can be realized in optical lattices with ultra-cold atoms or circuit-QED lattices with interacting photons. Such models have a lowest flat band in the single-particle spectrum. The flat band is spanned by eigenstates forming localized loops on the lattice, with the maximally compact loop states typically breaking the discrete rotational symmetry of the lattice. When populated by locally-interacting particles, the close packing of such maximally compact loop states leads to a nematic loop crystal ground state. We predict that increasing the filling beyond the close packing fraction leads to the formation of quantum liquid crystals including a nematic supersolid and a nematic superfluid phase. We also show how the nematicity can be probed by time-of-flight experiments or phase imprinting techniques [1].

In the second part, I discuss how 4-body spin interactions can emerge in a 2D flat-band lattice with “Aharonov-Bohm cages”, and in the presence of light-matter interactions.  Based on such an idea, one can realize the surface-code Hamiltonian in the ultra-strong coupling regime of a circuit-QED lattice, when the interaction strength is comparable to the microwave photon frequency.  Two types of 4-body stabilizer interactions are realized by utilizing the electro-magnetic duality in circuit-QED. In such case, the circuit-QED vacuum has topological degeneracies and can be used as a self-correcting quantum memory.   An alternative approach without ultra-strong coupling is to simulate the surface-code Hamiltonian in the rotating frame, with side-band driving through modulating the flux penetrating SQUID couplers.

[1]  Guanyu Zhu, Jens Koch and Ivar Martin,  arXiv:1411.0043

Spring 2015

4/15 Weds 2:30pm Ari Turner (John Hopkins)

Title: Spin Fluctuations and Entanglement

Abstract: I will compare the effects of quantum and thermal fluctuations in a spin chain by calculating the probability distribution for spin fluctuations in a segment. The calculation will use the concept of an "entanglement Hamiltonian." The entanglement Hamiltonian can be used to identify topological phases, but I will show that it is helpful for long-wavelength correlations as well as topological ones. The entanglement Hamiltonian is an imaginary system that describes the correlations of the ground state.  It cannot be measured directly, but it is related to the  statistics of the  fluctuations, so measuring the spin fluctuations of the atoms on the sites of an optical lattice is an indirect way of measuring the entanglement Hamiltonian.

3/26 Thurs 2:30pm Mark Hillery (Hunter College, CUNY)

Title: Quantum walks

Abstract:
A quantum walk is a quantum version of a random walk.  Instead of having a probability to move from one point to the next, the particle making the walk has an amplitude to do so, and this means that interference plays a role in quantum walks, whereas it does not in a standard random walk.  The walk can take place on a line or on a more general graph.  One of the motivations in studying quantum walks is to use them to find new quantum algorithms, and this effort has been successful.  The talk will focus on searches using quantum walks, and the description of quantum walks by means of scattering theory.

3/10 Tues 2:30pm Rajeev Singh (Max Planck, Dresden)

Title: Many-body localization and its signatures in quantum quenches

Abstract: The presence of disorder in a non-interacting system can
localize all the energy eigenstates, a phenomena dubbed Anderson
localization. Many-body localization is an extension of this phenomena
to include interactions. Effects of interactions show up in the
logarithmic growth of entanglement after a global quench. We perform a
systematic study of the evolution and saturation of entanglement and
show that it can be used to detect the localization transition. We
consider the bipartite fluctuation which also captures the transition
and is promising as an experimental probe. We compare these results to
that of a non-interacting system and note important differences
between the two.

2/26 Thurs 2:30pm Andrew Darmawan (Scherbrooke)

Title: Graph states as ground states of two-body frustration-free Hamiltonians

Abstract:
In measurement-based quantum computation (MBQC), universal quantum computation is realised in two main steps: preparing a special entangled state of many particles called a universal resource, then implementing an algorithm by measuring individual particles in the resource. A question of considerable recent research interest is whether there exist interacting spin systems with ground states that are universal resources for MBQC. While the original universal resource, the cluster state, has a number of appealing properties, it has been proven that it cannot arise as an exact ground state of a two-body Hamiltonian. In this talk I will explain how we can take certain two-body Hamiltonians (including the AKLT Hamiltonian), and deform them such that their ground states are arbitrarily close to universal graph states, while preserving two-bodiness and frustration-freeness. By deforming models in this way, we can observe transitions in computational power similar to physical phase transitions. In agreement with previous no-go results, we cannot obtain an exact graph state as a ground state, only an approximation, and there is a trade-off between the fidelity of the ground state and the gap of the Hamiltonian.

2/5 Thurs 2:30pm Dongling Deng (Michigan)

Title: Probe knots and Hopf insulators with ultracold atoms

Abstract: Knots and links are fascinating and intricate topological objects that have played a prominent role in physical and life sciences. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here, we show that knotted structures also exist in a peculiar class of three dimensional topological insulators---the Hopf insulators. In particular, we demonstrate that the spin textures of Hopf insulators in momentum space are twisted in a nontrivial way, which implies various knot and link structures. We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates. The extracted Hopf invariants, knots, and links are validated to be robust to typical experimental imperfections. Our work establishes the existence of knotted structures in cold atoms and may have potential applications in spintronics and quantum information processings.

Fall 2014

12/5 Fri 3:30pm Nicholas Valente  (SBU Math)

Title: Introduction to Quantum Complexity

Abstract: In this presentation we will introduce some of the core ideas in complexity theory such as Turing Machines, complexity classes, and complete problems. We will explore the complexity class NP, its quantum analogue QMA, and complete problems in each class. In particular we will show that the 3-SAT problem is NP-complete and how this generalizes to showing that the local Hamiltonian problem is QMA-complete.

12/3 Wed 1pm Kuei Sun (U. Texas at Dallas)
Title:  Spin-related superfluid phases in ultra-cold quantum gases

Abstract: I would like to present our recent study on novel superfluid phenomena in Bose-Einstein condensates (BEC) and degenerate Fermi gases (DFG) by engineering the spin degrees of freedom of ultra-cold atoms. In the bosonic case, we propose to realize spin and orbital angular momentum coupling in a BEC and study its ground state properties in a ring geometry. Such system is naturally subject to the angular momentum quantization and exhibits strong many-body physics in contrast with common spin-linear momentum coupled superfluids in experiments. In the fermionic case, we study spatially oscillatory pairing (Fulde–Ferrell–Larkin–Ovchinnikov or FFLO order) in DFG superfluid with spin imbalance, with focus on an experimental system in tubular optical lattices. We find the evolution of the FFLO order as the lattice depth varies and an interesting phase diagram for the unpaired majority spins. Our results could help the search for the elusive FFLO order, proposed about half century ago.

Refs: arXiv:1411.1737; PRA 87, 053622 (2013); PRA 85, 051607(R) (2012)

11/13 Thurs 2:30pm Zhengcheng Gu (Perimeter Institute)
Classification of symmetry protected topological order in interacting boson/fermion systems.

Abstract: Symmetry protected topological(SPT) phase is a generalization of topological insulator(TI). Different from the intrinsic topological phase, e.g., the fractional quantum hall(FQH) phase, SPT phase is only distinguishable from a trivial disordered phase when certain symmetry is preserved. Indeed, SPT phase has a long history in 1D, and it has been shown that the well known Haldane phase of S=1 Heisenberg chain belongs to this class. However, in higher dimensions, most of the previous studies focus on free/weakly interacting electron systems. Until very recently, it was realized that SPT phase also exists in interacting boson/spin systems in higher dimensions. In this talk, I will first discuss how to understand and characterize these phases through their seemingly featureless bulk properties. Then I will show how to use topological terms to classify these new class of quantum phases in interacting boson systems systematically in arbitrary dimension. With these topological terms, the gapless nature of edge states becomes manifested. The topological terms also issue the stability of SPT phases, regardless the strength of interactions, so long as the bulk gap is not closed and symmetry is unbroken. Finally, I will discuss the generalization of the classifying scheme for interacting fermion/electron systems, which leads to a new concept and mathematical framework – group supercohomology theory for fundamental physics.

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11/11 Tues 2pm Tianran Chen (West Chester University)
Why is the bulk resistivity of topological insulators so small?

Abstract. As-grown topological insulators (TIs) are typically heavily doped n-type crystals. Compensation by acceptors is used to move the Fermi level to the middle of the band gap, but even then TIs have a frustratingly small bulk resistivity. We show that this small resistivity is the result of band bending by poorly screened fluctuations in the random Coulomb potential. Using numerical simulations of a completely compensated TI, we find that the bulk resistivity has an activation energy of just 0.15 times the band gap, in good agreement with experimental data. At lower temperatures activated transport crosses over to variable range hopping with a relatively large localization length. Using this theory, we can also explain the anomalously small thermopower of topological insulators as measured in experiments.

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10/30 Thus 2:30pm Jeongwan Haah (MIT)
Topological quantum phases from error correcting codes

Abstract: A topologically ordered system has locally indistinguishable ground states that are robust under small perturbations. This property has made excitement in the quantum information science, for a possible
application to a self-correcting quantum memory device. However, in contact with heat reservoir, any previously known topological system in 3+1 dimensions or less has a deconfined excitation propagating through the system, which destabilizes the desired quantum memory.

In this talk, I will discuss an exotic lattice model in 3+1D, obtained by studying quantum error correcting codes. The model has robust ground state degeneracy and deconfined excitations. Exotic is that the excitation is completely immobile; a hopping term does not appear under any finite order perturbations. In addition, the degeneracy is interestingly a number-theoretic function of system size. Having a concrete model, I will investigate further possibilities, and show that in 3+1D there must be a deconfined excitation if the model is a translation-invariant quantum error correcting code and has locally indistinguishable degenerate ground states. The excitation can be
either mobile or immobile, and a sufficient condition will be given when it is mobile. The proof uses chain complexes over a Laurent polynomial ring, which might be of interest on its own.

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10/2 Thurs 2:30pm Lea Santos (Yeshiva)
"Relaxation and thermalization in isolated interacting quantum systems".

ABSTRACT: We consider one-dimensional isolated interacting quantum systems that are taken out of equilibrium instantaneously. Three aspects are addressed: (i) the relaxation process, (ii) the size of the temporal fluctuations after relaxation, (iii) the conditions to reach thermal equilibrium. The relaxation process and the size of the fluctuations depend on the interplay between the initial state and the Hamiltonian after the perturbation, rather than on the regime of the system. They may be very similar for both chaotic and integrable systems. The general picture associating chaos with the onset of thermalization is also further elaborated. It is argued that thermalization may not occur in the chaotic regime if the energy of the initial state is close to the edges of the spectrum, and it may occur in integrable systems provided the initial state is sufficiently delocalized.

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9/16 & 23 Tues 2:30pm Colin West on "MPS algorithms in the presence of symmetries"

9/9 Tues 2:30pm Abhishodh Prakash on "Quantum Phase transitions in Matrix Product States"

9/5 Friday 10am Maximilian Wagner on "Spin-Boson model and quantum synchronization"

Summer 2014

5/28 Wed: 11am Abhishodh Prakash

We look at ground states of certain quantum spin chains characterized by a nontrivial symmetry protected topological order. We explore the question of whether we can perform certain operations of measurement based quantum computation using only properties of the phase and not the parameters of the Hamiltonian. We see that we can prove the 'perfect' operation of the identity gate for a specific class of symmetries. We also briefly discuss nontrivial operations and generalization to any group.
References:
1) http://arxiv.org/abs/1201.4877
2) http://arxiv.org/abs/1207.4805

Spring 2014

--5/7 Wed 2:30pm Ian Affleck (UBC) [usual location: Math 6-125]
Title: Topological Superconductor - Luttinger liquid Junctions

Abstract: A spin-orbit coupled quantum wire, proximate to a superconductor, has a topological phase with Majorana modes localized at each edge of the superconductor. When the normal part of the wire has 2 channels coupled to the Majorana mode, and interaction effects are included, an unusual type of frustration occurs with a resulting quantum critical point. I will discuss how this might be probed experimentally to provide evidence for the topological phase.

--5/6 Tues 2:30pm Ian Affleck (UBC) [Note location at Simons Center 102]
Title: Quantum impurity problems and conformal field theory

Abstract: Models of a single quantum impurity interacting with a gapless continuum of delocalized excitations play an important role in condensed matter physics. The universal low energy properties of such models can quite generally be studied using boundary conformal field theory. This has led to non-trivial exact results for certain models such as the multi-channel Kondo problem but many physical models remain unsolved. I will give an overview of this subject.

--4/24 Thurs 2:30pm Ching-Yu Huang (MaxPlanck, Dresden)
"Classification of Topologically ordered Phases".

Abstract: Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry enriched topological (SET) phases. We introduce simple methods to detect the SET order directly from a complete set of topologically degenerate ground state wave functions. In particular, we first show how to directly determine the characteristic symmetry fractionalization of the quasiparticles from the reduced density matrix of the minimally entangled states. Second, we show how a simple generalization of a string order parameter can be measured to detect SET. The selection rules will get a characterization of SET. This way is more physical, and can be used by other methods, e.g., quantum Monte Carlo methods or potentially measured experimentally. We demonstrated the usefulness of this approach by considering a spin-1 model on the honeycomb lattice and the resonating valence bond state on a kagome lattice.

--3/11 Tues 2:30pm Sukhwinder Singh (Macquaire University)
Title: Entanglement renormalization, symmetries and holography

Entanglement renormalization is a real-space renormalization group (RG) transformation for quantum many-body systems. It generates the multi-scale entanglement renormalization ansatz (MERA), a tensor network capable of efficiently describing a large class of many-body ground states, including those of systems at a quantum critical point, or with topological order. In this talk I will describe recent applications of entanglement renormalization in the context of a RG based classification of symmetry protected phases in one dimension, and realizing aspects of the AdS/CFT correspondence on a lattice.

Based on: SS and Guifre Vidal, Physical Review B, 88, 121108 (Rapid communications) (2013).

--2/26 Wed 2:30pm. Hector Bombin (Perimeter Institute)
Title: Topological approach to quantum error correction

Abstract: It is essential to discover quantum error-correcting techniques with characteristics that can make quantum computing technology feasible. The line of research of topological codes has in this regard been very fruitful, as it has yielded prime candidates for implementing realistic scalable quantum computing architectures. This success is partially explained due to the connection of topological codes with condensed matter physics, which in addition has given rise to the notions of self-protected and self-correcting quantum memories. I will review several aspects of the subject and discuss a new family of topological codes with powerful features and that could possibly give rise to new physics.

--2/20 Thur 11am. Benjamin Brown (University of Leeds)
Fault-Tolerant Quantum Computation using Topological Defects

It is widely recognised that scalable quantum computation will require fault-tolerant protocols to deal with unwanted interactions with environmental degrees of freedom that will otherwise disturb the quantum phenomena we hope to exploit. A remarkable proposal for fault-tolerant quantum computation, topological quantum computation, encodes quantum information in robust non-local degrees of freedom of particles known as 'anyons'. More remarkably still, the information encoded over these special particles can be manipulated fault-tolerantly by braiding their world lines into non-trivial topologies. This mathematically elegant proposal is not just a theoretical pleasantry, but it is believed that anyonic particles can be realised as low energy excitations of topologically ordered lattice models. While this promises an exciting route towards an age of quantum technology, anyons are yet to be detected, and their realisation remains a challenging feat of engineering. Alternatively, it has recently been identified that defects in topologically ordered lattice models will also demonstrate some features that are analogous to anyonic particles. This presents an exciting new avenue towards quantum fault-tolerance. In this talk I will discuss topological quantum computation. We will go on to look at recent results in the area of topological defects, and examine the tools we can use to study them. Finally, we will consider the open questions in this field, and examine the prospects of developing a fault-tolerant quantum technologies by means of topology.

--2/12 Wed 11am, Henrik Johannesson (Gothenburg University)
TITLE:Topological insulators, helical electrons, and Rashba Interactions

ABSTRACT:
Topological insulators are new states of quantum matter characterized by an insulating gap in the bulk and gapless edge or surface states. These states – which give rise to the quantum spin Hall effect in two dimensions – are robust against time-reversal invariant perturbations when the electron-electron (e-e) interaction is strongly screened. However, for weak screening this property is lost. As a case in point I will discuss the effect of a Rashba spin-orbit interaction on the helical edge states of a quantum spin Hall insulator.  A Rashba coupling which is randomly fluctuating in space  – due to dopant ions at the quantum well interface – is found to open a scattering channel which causes localization of the edge modes. A periodic modulation of the Rashba coupling, produced by a periodic gating of the heterostructure, makes the edge insulating already at intermediate strengths of the e-e interaction [1]. Other surprising effects from the interplay between e-e and Rashba interactions is the suppression of the Kondo effect at the edge of a quantum spin Hall insulator [2], and the emergence of a ”synthetic” helical electron liquid in a quantum wire subject to a spatially modulated Rashba coupling [3].

[1] A. Ström, H. Johannesson, G. I. Japaridze, Phys. Rev. Lett. 104, 256804 (2010).

[2] E. Eriksson, A. Ström, G. Sharma, H. Johannesson, Phys. Rev. B 86, 161103(R) (2012).

[3] G. I. Japaridze, H. Johannesson, M. Malard, arXiv:1311.4716.

Fall 2013

Peter Love (Haverford): 10/22 (arrival)-10/25 (departure); seminar: 2:30pm, Wed. 10/23

Title: Mixed state entanglement: bounds, computation and optimal ensembles

Abstract: Quantifying entanglement has been a longstanding goal of quantum information theory, and many measures for pure states exist. These measures may be extended to mixed states by the convex roof construction. This requires the determination of the convex decomposition of the density matrix into pure states that minimizes the average pure state entanglement. One may regard this as the mean pure-state entanglement cost of synthesizing the density matrix. This minimization is challenging, and exact solutions are only known in a few cases, the most famous of which is the concurrence for two qubits. The next hardest case would seem to be the three-tangle for mixed states of three qubits, for which an analytic form is currently unknown. In this talk I will describe numerical techniques to both compute and bound the three-tangle, and give some properties of the minimal ensembles for this and other polynomial entanglement monotones.

Valentin Murg (Vienna): 11/3 (arrival) - 11/9 (departure); seminars: 4pm, Mon. 11/4 & 11am, Tue. 11/5

4pm Mon. 11/4 at S141 Physics building.
Title: Adiabatic Preparation of a Heisenberg Antiferromagnet Using an Optical
Superlattice

Abstract: We analyze the possibility to prepare a Heisenberg antiferromagnet with
cold fermions in optical lattices, starting from a band insulator and
adiabatically changing the lattice potential. The numerical simulation
of the dynamics in 1D allows us to identify the conditions for success,
and to study the influence that the presence of holes in the initial
state may have on the protocol. We also extend our results to
two-dimensional systems.

11am Tues. 11/5. Room 6-125 Math Tower (YITP Common Room)
Title: Compressed Simulation of evolutions of the XY-model

Abstract: We derive a quantum circuit processing log(n) qubits which simulates the
1D XY-model describing n qubits. In particular, we demonstrate how the
adiabatic evolution can be realized on this exponentially smaller system
and how the magnetization, which witnesses a quantum phase transition
can be observed. Furthermore, we analyze several dynamical processes,
like quantum quenching and finite time evolution and derive the
corresponding compressed quantum circuit.

Aram Harrow (MIT): 11/21 (arrival) - 11/22 (departure); seminar: 11am Fri 11/22

title:
Product-state approximation to ground states

abstract:

Hamiltonians that are sums of two-body interactions between spins can
be thought of as the quantum generalization of classical 2-CSPs
(constraint-satisfaction problems).  An important difference is that
the ground state of a Hamiltonian will generally be entangled and as a
result may fail to have a good short classical description.  But is
entanglement a property only of the ground state or can it be made to
be important even for states with low extensive energy?  The quantum
PCP (probabilistically checkable proof) conjecture and the NLTS (no
low-energy trivial state) conjecture both posit the existence of
Hamiltonians where even low-energy states must be highly entangled.
In this talk, I'll explain why such Hamiltonians (if they exist) must
involve only a small number of interactions per system (i.e. must be
defined on a low-degree graph).  This will follow by showing how
product states can approximate the ground-state energy of any
Hamiltonian on a high-degree graph, thus putting the corresponding
approximation problem in NP.  This result can be thought of as
removing the usual symmetry assumption from mean-field theory.

I will also prove that in many cases, low-energy product states not
only exist but can be found efficiently.  These cases include dense
hypergraphs, planar graphs and graphs whose adjacency matrices have
few large eigenvalues.

This is based on arXiv:1310.0017, which is joint work with Fernando Brandao.

Rolando Somma (Los Alamos): 12/11 (arrival) - 12/13 (departure); seminar: 2:30pm, Thur. 12/12

Exponential improvement in precision for Hamiltonian-evolution simulation

Abstract: I will present a quantum method for simulating Hamiltonian evolution with complexity polynomial
in the logarithm of the inverse error. This is an exponential improvement over existing methods for
Hamiltonian simulation. In addition, its scaling with respect to time is close to linear, and its scaling
with respect to the time derivative of the Hamiltonian is logarithmic. These scalings improve upon
most existing methods. Our method is to use a compressed Lie-Trotter formula, based on recent
ideas for efficient discrete-time simulations of continuous-time quantum query algorithms.

This is joint work with Dominic Berry, Andrew Childs, Richard Cleve and Robin Kothari.

Spring 2013

--- Thurs, Apr 18, 2013, 2:30pm at YITP Common Room
Oliver Buerschaper, TBA

--- Thurs, Apr 11, 2013, 3:00pm at YITP Common Room (YITP, notice special time)
Robert Raussendorf on "Contextuality in Measurement-based Quantum Computation"

Abstract: In this talk, I discuss the interplay between contextuality (a special form of non-classicality) and computational power in measurement-based quantum computation (MBQC). I begin by reviewing a first example of this connection due to Anders and Browne [1], in which a simple proof of the Kochen-Specker theorem [2] due to D. Mermin [3] is re-purposed as an MBQC. Generalizing this example we show--under assumptions that are natural for qubit systems--that measurement-based quantum computations (MBQCs) which compute a non-linear Boolean function with high probability are contextual. The class of contextual MBQCs includes an example which is of practical interest and has a super-polynomial speedup over the best known classical algorithm, namely the quantum algorithm that solves the ‘Discrete Log’ problem.

[1] J. Anders and D.E. Browne, Phys. Rev. Lett. 102, 050502 (2009).

[2] S. Kochen, and E.P. Specker, J. Math. Mech. 17, 59 (1967).

[3] N. D. Mermin, Rev. Mod. Phys. 65, 803 (1993).

--- Wed, Mar 27, 2013, 11am at YITP Common Room
Erik Eriksson (Gothenburg) on "Generalized Gibbs ensembles and the one-dimensional Bose gas"

Abstract:
We discuss the concept of a generalized Gibbs ensemble for the relaxation of integrable systems, and apply it to the Lieb-Liniger model describing a one-dimensional interacting Bose gas. The usual Bethe-Ansatz solution is extended to capture low-energy excitations for a generalized dispersion relation, and conformal field theory is applied to extract correlation functions from the finite-size corrections [Eriksson & Korepin, arXiv:1302.3182]

--- Mon, Mar 25, 2013, 2pm at YITP Common Room (YITP Seminar)

Dimitris G. Angelakis (Technical University of Crete/Centre for Quantum Technologies) on "Quantum simulations with photons: The path from Mott transitions to interacting relativistic theories with light"

Abstract: I will start by reviewing the founding works in the novel field of photonic quantum simulations, and present the ideas for observing photon-blockade induced Mott transitions in coupled cavity QED systems [1]. After briefly touching on the idea of simulating spin-models and the Fractional Hall effect [2] with photons, I will talk about the more recent developments in realizing continuous 1D models in nonlinear optical fibers exhibiting electromagnetically induced transparency nonlinearities. Here the concept of the  "photonic Luttinger liquid" will be introduced, along with a proposal to observe spin-charge separation with polarized photons in a nonlinear slow light set up based in a fiber interfaced with cold atoms[3].

I will continue by presenting our recent efforts in simulating 1D lattice models in the non-relativistic regimes, such as the sine-Gordon and Bose-Hubbard[4] and the efforts for simulations of out of equilibrium phenomena using driven systems[5]. I will conclude by presenting ongoing work on interacting relativistic models (Thirring) using polarized photons[6]. Possible experimental implementations in quantum optical systems such as photonic crystals, optical fibers coupled to cold atoms, and Circuit QED will be discussed.

1) DGA, M. F. Santos, S. Bose, “Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays”, Phys. Rev. A (Rap. Com.) vol. 76, 031805 (2007); New Scientist 13 January 2007, p. 42.

2) J. Cho,  DGA, S. Bose, “Fractional Quantum Hall state in coupled cavities”. Phys. Rev. Lett. 101, 246809 (2008)
3) DGA, M. Huo, E. Kyoseva, LC Kwek, “A photonic Luttinger liquid and spin-charge separation in a quantum optical system''.Phys. Rev. Lett. 106, 153601 (2011); See also Viepoint in Physics, by Gregory Fiete "In a tight spot, spin and charge separate ", Physics 4, 30 (2011) ; Nature Research Highlights: "Optical Physics: A liquid of photons", Nature, 472, 262 (2011)

4)  M. Huo, DGA “sine Gordon and Bose-Hubbard dynamics with photons in a nonlinear fiber''.Physical Review A 85, 023821 (2012)

5) T. Gruzic, S. R. Clark. D. G. Angelakis. Dieter Jacksh "Non-equilibrium many-body effects in driven nonlinear resonator arrays", arXiv:1205:0994 , New Journal of Physics,  14 103025 (2012); Changsuk Noh, Blas M. Rodriguez, Dimitris G.  Angelakis "Realizing the driven non-linear Schrodinger equation with stationary light", arXiv:1208.0313

6) DGA, M. Huo, D. Chang, L C Kwek, V. Korepin "Mimicking interacting relativistic theories with stationary light" arXiv:1207.7272 (to appear in PRL)

--- Wed, Mar 13, 2013, 11am at YITP Common Room
Raul Santos on "Entanglement and Boundary Theories"

Abstract: In the ground state of gapped systems, the entanglement entropy of a subsystem A scales with the length of the boundary of A. This observation suggest that the entanglement properties of the subsystem can be described in terms of degrees of freedom living in the boundary of A. In this talk I will review the the connection between entanglement properties and effective boundary descriptions in topological and spin systems.

--- Thur, Mar 7, 2013, 2:30pm at YITP Common Room (YITP Seminar)
Sergey Bravyi (IBM Watson) on "Criticality without frustration for quantum spin-1 chains"

Abstract: Frustration-free (FF) spin chains have a property that their ground state minimizes all individual terms in the chain Hamiltonian. We ask how entangled the ground state of a FF quantum spin-s chain with nearest-neighbor interactions can be for small values of s. While FF spin-1/2 chains are known to have unentangled ground states, the case s=1 remains less explored. We propose the first example of a FF translation-invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of a critical behavior. The ground state can be viewed as the uniform superposition of balanced strings of left and right parentheses separated by empty spaces. Entanglement entropy of one half of the chain scales as log(n)/2 + O(1), where n is the number of spins. We prove that the energy gap above the ground state is polynomial in 1/n. The proof relies on a new result concerning statistics of Dyck paths which might be of independent interest.

--- Fri, Feb 15, 2013, 11am at YITP Common Room (YITP Seminar)
Valentin Murg (University of Vienna) on "Tensor Network Methods in Quantum Chemistry"

Abstract: We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Extending the matrix-product-state picture, we formulate a more general approach by allowing the local sites to be coupled to more than two neighboring auxiliary subspaces. Calculations carried out on small quantum chemical systems support our approach.

Fall 2012

--- Wed, Sep 26, 2012, 2:30pm at
YITP Common Room (YITP Seminar)
Luigi Amico (Catania) will speak on "Entanglement transition in quantum magnets"

Abstract.
Entanglement is a defining feature of quantum mechanics that in recent years has led to the development of the new discipline of quantum information theory. Its application to spin systems predicts a new type of zero temperature transition in an applied magnetic field at which the nature of the entanglement qualitatively changes without any anomaly  in the ground state energy of the system. I will discuss the correlations near such an entanglement transition. I will report on the first attempt to observe the phenomenon with a neutron scattering experiment in a one
dimensional quantum magnet.

--- Tue, Sep 18, 2012, 11:00am at YITP Common Room
Erik Eriksson (Gothenberg) will speak on "Electrical control of the Kondo effect in a helical edge liquid"

Abstract:
Magnetic impurities affect the transport properties of the helical edge states of quantum spin Hall insulators by allowing single-electron backscattering. We study such a system in the presence of a Rashba spin-orbit interaction induced by an external electric field, showing that this can be used to control the Kondo temperature, as well as the correction to the electrical conductivity due to the impurity. In particular, the impurity contribution to the dc conductivity can be switched on and off by properly adjusting the strength of the Rashba coupling. Furthermore, in certain regimes our perturbative renormalization-group analysis suggests the Kondo singlet formation might be completely destroyed by the Rashba interaction. will speak on "Towards unconventional symmetries in tensor network states"

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Thu, Sep 6, 2012, 2:30pm at YITP Common Room (YITP Seminar)
Oliver Buerschaper (Perimeter Institute) will speak on "Towards unconventional symmetries in tensor network states"

Abstract: We report on unconventional symmetries in tensor network states and their implications for topological order.

past meetings, Spring 2012

--- Thu, April 26, 2012, 2:30pm at YITP Common Room (YITP Seminar)
Chris Laumann (Harvard) will speak on " Disorder-induced phases of interacting non-Abelian anyons"

Abstract:
Phases of matter exhibiting non-Abelian anyonic quasiparticles provide the foundation for topological quantum computing. Such quasiparticles are also of intrinsic interest as they deviate from the conventional classification of bosons and fermions. In bulk samples, a finite density of quasiparticles naturally arises, naively producing an extensive topologically protected ground state entropy. Microscopic interactions generically lift this degeneracy producing descendant' phases of interacting anyons, much as residual exchange interactions lift the extensive spin degeneracy associated with a Mott insulator to produce magnetic order.

In this talk, I will review the physics of pinned, interacting anyons and their known translation-invariant phases and then consider the effects of quenched spatial disorder, as arises naturally in realistic samples. In one spatial dimension, such disordered anyon models have previously been shown to exhibit a hierarchy of infinite randomness phases under a strong-disorder renormalization group (SDRG) approach. I will address systems in two spatial dimensions and show that the flow to infinite randomness of Ising and Fibonacci anyons does not survive by developing a planar SDRG approach to handle the topology-dependent interactions generated during the flow.

Using the alternative approach of fermionization, available only for the Ising case, we will instead discover that moderate disorder induces a thermally conducting metallic phase. I will highlight the implications of this finding for the experimental search for anyons in the $\nu=5/2$ fractional quantum Hall state.

Refs:
CRL, Ludwig, Huse and Trebst. Phys. Rev. B 85, 161301(R) (2012). arXiv:1106.6265.
CRL, Huse, Ludwig, Refael, Trebst and Troyer. arXiv:1203.3752.

--- Thu, April 19, 2012, 4:00pm at YITP Common Room
Vladimir Goldman will speak on "Laughlin (FQHE) quasiparticles as realization of anyons in nature"

--- Fri, April 13, 2012, 3:00pm at YITP Common Room
Dominik Schneble will speak on "Excitations and transport in 1D bosonic mixtures"

--- No meeting on Thu, April 5, 2012, Spring recess

--- Thu, Mar. 29, 2012, 4:00pm at YITP Common Room
Mathew Madhavacheril  will speak on "Entanglement Entropy in Conformal Field Theories"

Abstract:In this talk, we will go through the field-theoretic derivation of the scaling of entanglement entropy in CFTs. I will mainly be focusing on 1+1 CFTs, presenting two ways of obtaining the logarithmic scaling of entropy with length of the system. Both methods are based on the 'replica' trick. The first is a calculation from the conformal dimension of twisted operators on the complex plane. The second method is a geometric derivation from the Weyl anomaly, which is extendable to 4D CFTs that show an area scaling, and in which the relation of entropy to 'a' and 'c' central charges becomes especially interesting. In the 2D case, I will also briefly touch on other geometries, finite temperature and massive theories if time permits, and brief mention will be made of a relatively new and easier "holographic" derivation.

--- Wed, Mar. 28, 2012, 2:30pm at YITP Common Room (YITP Seminar)
Valentin Murg (Vienna)   will speak on "Numerical simulations with tensor network states"

Abstract: Numerical simulations with tensor network states are applied to two-dimensional systems and quantum chemical systems.

--- Thu, Mar. 22, 2012, 4:00pm at YITP Common Room
Francis Paraan  will speak on "
Entanglement in q-deformed valence-bond-solid states"

Abstract: In this talk I will continue our discussion on the entanglement in q-deformed valence-bond-solid (VBS) states. After reviewing the properties of the q-deformed SU(2) algebra, I will define the generalized Affleck-Kennedy-Lieb-Tasaki (AKLT) model. I will construct the VBS ground state of this model and write its matrix product state (MPS) representation. I then calculate the reduced density matrix of a contiguous block of spins in this state. I will use the eigenvalues of this matrix to obtain the entanglement spectrum and entropy of the block. Effective thermal ensembles with the same spectrum as the reduced density matrix will be presented. The temperature of these effective models will be expressed in terms of the deformation parameter q.

--- Thu, Mar. 15, 2012, 5:00pm at YITP Common Room (notice time)
Erik Eriksson (Göteborgs university, Sweden) will speak on "Entanglement entropy in Kondo systems from CFT"

Abstract: In this talk the conformal-field-theory technique for calculating entanglement entropy will be briefly introduced, and new results for the scaling corrections from boundary perturbations will be presented. This can be applied to the study of entanglement in Kondo systems, where electrons interact with magnetic impurities to form a "screening cloud" and where the low-energy behavior can be described by a boundary CFT. Our results for the entanglement entropy therefore give the large-distance asymptotic behavior of the screening cloud. We also discuss the relation to the thermodynamics of the impurity.

--- Thu, Mar. 15, 2012, 11:00am at YITP Common Room (special seminar)
Francis Song (Yale) will speak on "Entanglement in Quantum Many-Body Systems"

Abstract: The scaling of entanglement entropy, and more recently the full entanglement spectrum, have become useful tools for characterizing certain universal features of quantum many-body systems. We motivate the importance of entanglement in the study of many-body systems by considering the “gratuitously big” size of Hilbert space and the need for generic ansatzes that efficiently represent useful wave functions. In addition, we study the scaling of the entanglement entropy in the two-dimensional spin-1/2 Heisenberg antiferromagnet, where our work and other recent work indicate that a subleading logarithmic term contains universal information about the number of Goldstone modes in the symmetry-broken phase. Although entanglement entropy is difficult to measure experimentally, we show that for systems that can be mapped to non-interacting fermions both the von Neumann entanglement entropy and generalized R\'{e}nyi entropies can be related exactly to the cumulants of number fluctuations, which are accessible experimentally. In principle, this also extends to the full entanglement spectrum. Such systems include free fermions in all dimensions, the integer quantum Hall states and topological insulators in two dimensions, strongly repulsive bosons in one-dimensional optical lattices, and the spin-1/2 XX chain, both pure and strongly disordered. The same formalism can be used for analyzing entanglement entropy generation in quantum point contacts with non-interacting electron reservoirs. Beyond the non-interacting case, we show that in analogy to the full counting statistics used in mesoscopic transport, fluctuations give important information about many-body systems including the location of quantum critical points.

--- Thu, Mar. 8, 2012, 2:30pm at YITP Common Room (YITP seminar)

Stephen Jordan (NIST) will speak on "Quantum Algorithms for Quantum Field Theories"

Abstract: Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. I will discuss a polynomial-time quantum algorithm for simulating a quantum field theory, which I developed in collaboration with Keith Lee and John Preskill. Such simulations are believed to require exponential time on classical computers. No prior knowledge of quantum algorithms or quantum field theory will be assumed.

--- Thu, Mar. 8, 2012, 11 am at YITP Common Room (special seminar)

Artur Garcia Saez (Barcelona) will speak on "Solving physical and computational problems using tensor-network contractions"

Abstract: The representation of quantum states using low-rank tensor networks allows for an efficient study of computational models and condensed-matter systems. We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy and can be applied to three dimensional condensed-matter systems. The underlying rational for emphasizing the exact coarse graining renormalization group step prior to truncation is related to monogamy of entanglement.

--- Thu, Feb. 23, 2012, 4pm at YITP Common Room

Raul Santos will speak on "Standard and q- deformed spin 1 AKLT model"

Abstract: In this talk I will review in detail the standard (SU(2)) invariant Affleck Kennedy Lieb Tasaki model (AKLT) in one dimension. I will show the representation of the valence bond solid (VBS) ground state in terms of Schwinger boson representation and the dimension of the ground space (for different boundary conditions). I will deduce the matrix product state representation for this state and generalize it to the q-deformed SU(2) algebra. In this generalized model I will show
the dependence of the entanglement spectrum on the deformation parameter.

References:

I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki,
Phys. Rev. Lett. 59, 799 (1987).
http://dx.doi.org/10.1103/PhysRevLett.59.799

R. A. Santos, F. N. C. Paraan, V. Korepin, A. Klümper
arXiv:1112.0517

--- Thu, Feb. 16, 2012, 4pm at YITP Common Room

Petr Anisimov will continue on "Introduction to Quantum Metrology "(Part II)

--- YITP seminar: Wed, Feb. 15, 2012, 2:30pm at YITP Common Room
Ramis Movassagh (MIT) on "Density of States of Quantum Spin Systems from Isotropic Entanglement"

Abstract: We propose a method which we call "Isotropic Entanglement" (IE), that predicts the eigenvalue distribution of quantum many body (spin) systems (QMBS) with generic interactions. We interpolate between two known approximations by matching fourth moments. Though, such problems can be QMA-complete, our examples show that IE provides an accurate picture of the spectra well beyond what one expects from the first four moments alone. We further show that the interpolation is universal, i.e., independent of the choice of local terms. Ref: Phys. Rev. Lett. 107, 097205 (2011)

--- Thu, Feb. 9, 2012, 4pm at YITP Common Room
Petr Anisimov on "Introduction to Quantum Metrology "

Abstract: At large, science as we know it is based on empirical knowledge. Thus there is no surprise that new high precision measurements are always taking the lead by offering new exploration frontiers. In the past, increase in precision came from a brute force approach that was offering improved accuracy of measurements by utilizing more resources. Laser interferometer gravitational-wave observatory is the most prominent example of such an approach.

It is a relatively recent development in precision metrology to focus on a different approach that utilizes quantum mechanics for
improvement of measuring precision provided limited resources. Starting with some interesting examples, I will present my
understanding of the current state of Quantum Metrology. I will discuss two interesting questions that are relevant to the field in
relation to the fundamental limitations of quantum metrology:
1.    given a fixed amount of resources, what is the best possible precision achievable in principle, that is, the precision that we
aspire to reach?
2.    (given a physical setup), what is the precision that is actually obtained?
I will walk you through the answers to these questions that were found during my work at Louisiana State University.

Fall 2011 Semester

--- Fri, Dec. 9, 2011, 3pm at YITP Common Room

Colin West on "Quantum Computation and the Evaluation of Tensor Networks"

Abstract: I present recent work by Arad and Landau, giving an efficiently implementable algorithm which approximates the value of a completely contracted tensor network. The existence of this algorithm gives a significant result about the complexity of evaluating tensor networks, which is shown to be a complete problem for quantum computation. As a result, tensor networks can be viewed as an alternative way to visualize quantum circuits, while opening the door to other circuits which would previously have been considered unimplementable. One such scheme to estimate the partition function of any q-state thermodynamic model will be shown.
Ref: arXiv:0805.0040

--- Fri, Dec. 2, 2011, 3pm at YITP Common Room
You Quan Chong on "Introduction to quantum discord"

Abstract:  Quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. Quantum discord was introduced in 2001 by Harold Ollivier and Wojciech H. Zurek. It includes correlations that are due to quantum effects but do not necessarily involve quantum entanglement. I will introduce the definition of quantum discord and some of the recent findings that highlight its usefulness in quantifying the correlations in a bipartite system.

--- Fri, Nov. 18, 2011, 3pm at YITP Common Room (Math 6-125):
Adrian Soto on "Exact solution to 3SAT using tensor networks"

Abstract: "3SAT is a fundamental problem in computer science and complexity theory. An exact tensor network solution to this problem has recently been proposed. This tensor network delivers an unnormalized quantum state whose coefficients encode all the solutions to the 3SAT instance, if any. Furthermore, the tensor network also solves the problem of counting the number of solutions to a particular 3SAT instance. I will introduce the 3SAT problem and I will construct explicitly the proposed tensor network. Alternatively, it will be shown that this quantum state can be seen as the ground state of a spin system Hamiltonian. I will also explain how to obtain a particular satisfying assignment to the 3SAT instance by contracting the tensor network as many times as there are bits involved in the instance."

Ref. A. Garcia-Saez and J. I. Latorre, arXiv: 1105.3201v2

--- Fri, Nov. 4, 2011,
3pm at YITP Common Room (Math 6-125):
Andreas Kluemper (Wuppertal University, Germany) continues on "Diagrammatics for su(2) invariant matrix product states"

--- Fri, Oct.28, 2011, 2:40pm at YITP Common Room (Math 6-125):
Andreas Kluemper (Wuppertal University, Germany) on "Diagrammatics for su(2) invariant matrix product states"

Abstract: Matrix product states (MPS) appear in different, but closely related ways. In the first part of my talk I will give a short review on (i) 'matrix-product ground-states' for a certain class of quantum spin Hamiltonians on lattices, (ii) 'vertex operators' appearing in the study of integrable systems, and (iii) states produced by 'density matrix renormalization group' calculations. In short: practically all equilibrium states are of MPS type.  In the second part of my talk I will present an application of the general MPS  structure of equilibrium states to the calculation of the ground-state properties of a quantum spin-1/2 chain with su(2) invariance. Systematic use  is made of the su(2) symmetry at all steps of the calculations: (i) the matrix  space is set up as a direct sum of irreducible representations, (ii) the local  matrices with state-valued entries are set up as superposition of su(2)  singlet operators, (iii) products of operators are evaluated algebraically by  making use of identities for 3j and 6j symbols. The explicit numerical results have accuracy better than 10^{-4} for nearest- and next-nearest neighbour spin  correlators and for general dimer-dimer correlators in the thermodynamical  limit of the spin-1/2 Heisenberg chain with frustration.

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--- Fri, Oct 14, 2011, 3pm at YITP Common Room:
Tzu-Chieh Wei concludes on "Introduction to Matrix Product States and Tensor Product States"

--- Thur, Oct 6, 2011, 4pm at YITP Common Room:
Tzu-Chieh Wei continues on "Introduction to Matrix Product States and Tensor Product States"

--- Fri, Sep 30, 2011, 3pm at YITP Common Room:
Tzu-Chieh Wei on "Introduction to Matrix Product States and Tensor Product States"

--- Thur, Sep 22, 2011, 4pm at YITP Common Room: Kick-off meeting