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Some Results of Vladimir Korepin

Quantum Field Theory

Semi-classical quantization of sine Gordon: → φtt - φxx +m2 sin(φ)= 0.

Quantum Inverse Scattering Method

Vertex Models of Statistical Mechanics

Correlation Functions in exactly solvable models

Hubbard Model in One Dimension

Supersymmetric extension

Quantum Entanglement

AKLT and VBS

  • Entanglement in a Valence-Bond-Solid State H. Fan, V. Korepin, V. Roychowdhury, Physical Review Letters, vol 93, issue 22, 227203, 2004
    The reduced density matrix of a continuous block of spins [of arbitrary length] has rank four. In the limit of large block the density matrix is proportional to a projector to degenerated ground state of a 'block' Hamiltonian [a part of original Hamiltonian describing interaction of spins inside of the block]. Both von Neumann entropy and Renyi entropy of large block of spins is ln(4).
  • Valence Bond Solid in Quasicrystals by A. Kirillov and V. Korepin, ALGEBRA and ANALYSIS , vol 1, issue 2, page 47, 1989
    A version of AKLT is constructed with unique VBS ground state on a finite graph .
  • ENTANGLEMENT IN VALENCE-BOND-SOLID STATES
  • Quantum Search Algorithms

    Lieb-Liniger Model of One Dimensional Anyons

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