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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.

------------------------------------------------------------------------------

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.

------------------------------------------------------------------------------

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.

------------------------------------------------------------------------------

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.

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"

--- 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.

--- 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