# Quantum Inverse Scattering Method and Correlation Functions

@inproceedings{Korepin1993QuantumIS,
title={Quantum Inverse Scattering Method and Correlation Functions},
author={Vladimir E. Korepin and A.G.Izergin and N.M.Bogoliubov},
year={1993}
}
• Published 25 January 1993
• Physics
One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References.
1,636 Citations
Connection between Yangian symmetry and the quantum inverse scattering method
• Physics
• 1996
The quantum nonlinear Schrodinger model with two-component fermions exhibits a Yangian symmetry when considered on an infinite interval. We construct the generators of the Yangian using Dunkl
Integral equations for correlation functions of a quantum one-dimensional Bose gas
The large-time, long-distance behavior of the temperature correlation functions of a quantum one-dimensional Bose gas is considered. We obtain integral equations, which are closely related to the
Temperature correlators in the two-component one-dimensional gas
• Physics, Mathematics
• 1998
Abstract The quantum non-relativistic two-component Bose and Fermi gases with infinitely strong point-like coupling between particles in one space dimension are considered. Time- and
Correlators in the one-dimensional two-component Bose and Fermi gases
• Physics
• 1997
Abstract Quantum nonrelativistic two-component Bose and Fermi gases with an infinitely strong δ -function interaction between particles are considered. The two-point correlation functions depending
Yangian Symmetry of the δ-Function Fermi Gas
• Physics
• 1996
The quantum nonlinear Schrodinger model with two-component fermions exhibits a Yangian symmetry when considered on an infinite interval. We construct the generators of the Yangian using one
Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations
• Physics, Mathematics
• 2003
We calculate exactly matrix elements between states that are not eigenstates of the quantum XY model for general anisotropy. Such quantities therefore describe non equilibrium properties of the
Dynamical correlation functions of the XXZ model at finite temperature
Combining a lattice path integral formulation for thermodynamics with the solution of the quantum inverse scattering problem for local spin operators, we derive a multiple integral representation for
One dimensional gas of bosons with integrable resonant interactions
We develop an exact solution to the problem of one dimensional chiral bosons interacting via an s-wave Feshbach resonance. This problem is integrable, being the quantum analog of a classical two-wave
Solution of quantum integrable systems from quiver gauge theories
• Physics
• 2015
A bstractWe construct new integrable systems describing particles with internal spin from four-dimensional N$$\mathcal{N}$$ = 2 quiver gauge theories. The models can be quantized and solved exactly
Ground state correlations of the quantum Toda lattice
Abstract Based on the Bethe ansatz equation and the finite-size scaling analysis of conformal field theory, we calculate critical exponents of the ground state correlations of the quantum Toda

## References

SHOWING 1-10 OF 14 REFERENCES
The quantum inverse scattering method approach to correlation functions
• Mathematics
• 1984
The inverse scattering method approach is developed for calculation of correlation functions in completely integrable quantum models with theR-matrix of XXX-type. These models include the
Lattice versions of quantum field theory models in two dimensions
• Physics
• 1982
Abstract The quantum inverse scattering method allows one to put quantum field theory models on a lattice in a way which preserves the dynamical structure. The trace identifies are discussed for
Calculation of norms of Bethe wave functions
A class of two dimensional completely integrable models of statistical mechanics and quantum field theory is considered. Eigenfunctions of the Hamiltonians are known for these models. Norms of these
Pauli principle for one-dimensional bosons and the algebraic bethe ansatz
• Mathematics
• 1982
For the construction of the physical vacuum in exactly solvable one-dimensional models of interacting bosons it is important that the momenta of all the particles be different. We give a formal proof
Momentum Distribution in the Ground State of the One-Dimensional System of Impenetrable Bosons
Girardeau has shown that an exact analytical formula may be given for the ground‐state wave‐function of a system of one‐dimensional impenetrable bosons. Starting with this formula, we give a
Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction
• Physics
• 1969
The equilibrium thermodynamics of a one‐dimensional system of bosons with repulsive delta‐function interaction is shown to be derivable from the solution of a simple integral equation. The excitation
EXACT ANALYSIS OF AN INTERACTING BOSE GAS. I. THE GENERAL SOLUTION AND THE GROUND STATE
• Physics
• 1963
A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum
We continue the analysis of the one-dimensional gas of Bose particles interacting via a repulsive delta function potential by considering the excitation spectrum. Among other things we show that: (i)
The most general L operator for the R-matrix of the XXX model
• Mathematics
• 1984
The problem of describing all the monodromy matrices for R matrices of the XXX and XXZ models is discussed. It is shown that the L operator of the lattice nonlinear Schrödinger model generates all
Study of Exactly Soluble One-Dimensional N-Body Problems
In this paper it is shown that several cases of one‐dimensional N‐body problems are exactly soluble. The first case describes the motion of three one‐dimensional particles of arbitrary mass which