Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0703319 · Journal of Physics A Mathematical and Theoretical

Dynamical correlation functions of theXXZmodel at finite temperature

Kazumitsu Sakai

Published Jun 19, 2007• 34 citations
arXivHTMLPDF

Abstract

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 the time-dependent longitudinal correlation function of the spin-1/2 Heisenberg XXZ chain at finite temperature and in an external magnetic field. Our formula reproduces the previous results in the following three limits: the static, the zero-temperature and the XY limits.

DOI
10.1088/1751-8113/40/27/007

Related papers

Integral representations for correlation functions of theXXZchain at finite temperature

Frank Göhmann, Andreas Klümper, Alexander Seel

We derive a novel multiple integral representation for a generating function of the $\s^z$-$\s^z$ correlation functions of the spin-$\2$ XXZ chain at finite temperature and finite, longitudinal magnetic field. Our work combines algebraic Bethe ansatz techniques for the calculation of matrix elements with the quantum transfer matrix approach to thermodynamics.

arXiv:hep-th/0405089•Journal of Physics A Mathematical and General•Jul 22, 2004•201 citations

Correlation functions of an interacting spinless fermion model at finite temperature

Kohei Motegi, Kazumitsu Sakai

We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems, the equal-time one-particle Green's function at arbitrary particle density is expressed as a multiple-integral form. Our formula reproduces previously known results in the following three limits: the zero-temperature, the infinite-temperature and the free fermion limits.

arXiv:0712.1399•Journal of Statistical Mechanics Theory and Experiment•Feb 11, 2008•0 citations

Correlation functions of an interacting spinless fermion model at finite temperature

Kohei Motegi, Kazumitsu Sakai

We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems, the equal-time oneparticle Green’s function at arbitrary particle density is expressed as a multiple integral form. Our formula reproduces previously known results in the following three limits: the zero-temperature, the infinite-temperature and the free fermion limits. PACS numbers: 05.30.-d, 71.10.Fd, 02.30.Ik 1

•Jan 1, 2008•0 citations

Correlation Functions of Quantum Integrable Models: The XXZ Spin Chain

Jean Michel Maillet

A general approach to the computation of exact correlation functions of lattice quantum integrable models proposed recently is reviewed. It is based on the resolution of the quantum inverse scattering problem. The application of this method to theXXZ Heisenberg spin- $$\tfrac{1}{2}$$ in a magnetic field leads to multiple integral representations of its n-point correlation functions. For zero magnetic field, it gives a proof, in both the massless and massive (anti-ferromagnetic) regimes, of the formulas obtained from the q-deformed KZ equations (massless regime) and the representation theory of the quantum affine algebra $${\mathcal{U}_q}(\widehat s{l_2})$$ together with the corner transfer matrix approach (massive regime). We also discuss further problems, related in particular to long distance asymptotics of these correlation functions.

Birkhäuser Boston eBooks•Jan 1, 2002•0 citations

Correlation functions of the higher spinXXXchains

N Kitanine

Using the algebraic Bethe ansatz, we consider the correlation functions of the integrable higher spin chains. We apply a method recently developed for the spin ½ Heisenberg chain, based on the solution of the quantum inverse problem. We construct a representation for the correlation functions on a finite chain for arbitrary spin. Then we show how the string solutions of the Bethe equations can be considered in the framework of this approach in the thermodynamic limit. Finally, a multiple integral representation for the spin 1 zero-temperature correlation functions is obtained in the thermodynamic limit.

arXiv:math-ph/0104016•Journal of Physics A Mathematical and General•Sep 21, 2001•41 citations

On the algebraic Bethe Ansatz approach to the correlation functions of the XXZ spin-1/2 Heisenberg chain(Solvable Lattice Models 2004 : Recent Progress on Solvable Lattice Models )

N Kitanine, Jean Michel Maillet, N. A. Slavnov +1 more

We present a review of the method we have elaborated to compute the correlation functions of the $XXZ$ spin-1/2 Heisenberg chain.This method is based on the resolution of the quantum inverse scattering problem in the algebraic Bethe Ansatz bamework, and leads to a mul- tiple integral representation of the dynamical correlation functions.We describe in particular some recent advances concerning the two-point functions: in the finite chain, they can be expressed in terms of a single multiple integral.Such a formula provides a direct analytic connection between the previously obtained multiple integral representations and the form factor expansions for the correlation functions.

数理解析研究所講究録•Apr 1, 2006•5 citations
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 the time-dependent longitudinal correlation function of the spin-1/2 Heisenberg XXZ chain at finite temperature and in an external magnetic field. Our formula reproduces the previous results in the following three limits: the static, the zero-temperature and the XY limits.
We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems, the equal-time one-particle Green's function at arbitrary particle density is expressed as a multiple-integral form. Our formula reproduces previously known results in the following three limits: the zero-temperature, the infinite-temperature and the free fermion limits.
We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems, the equal-time oneparticle Green’s function at arbitrary particle density is expressed as a multiple integral form. Our formula reproduces previously known results in the following three limits: the zero-temperature, the infinite-temperature and the free fermion limits. PACS numbers: 05.30.-d, 71.10.Fd, 02.30.Ik 1
A general approach to the computation of exact correlation functions of lattice quantum integrable models proposed recently is reviewed. It is based on the resolution of the quantum inverse scattering problem. The application of this method to theXXZ Heisenberg spin- 12\tfrac{1}{2}21​ in a magnetic field leads to multiple integral representations of its n-point correlation functions. For zero magnetic field, it gives a proof, in both the massless and massive (anti-ferromagnetic) regimes, of the formulas obtained from the q-deformed KZ equations (massless regime) and the representation theory of the quantum affine algebra Uq(s^l2){\mathcal{U}_q}(\widehat s{l_2})Uq​(sl2​) together with the corner transfer matrix approach (massive regime). We also discuss further problems, related in particular to long distance asymptotics of these correlation functions.
Using the algebraic Bethe ansatz, we consider the correlation functions of the integrable higher spin chains. We apply a method recently developed for the spin ½ Heisenberg chain, based on the solution of the quantum inverse problem. We construct a representation for the correlation functions on a finite chain for arbitrary spin. Then we show how the string solutions of the Bethe equations can be considered in the framework of this approach in the thermodynamic limit. Finally, a multiple integral representation for the spin 1 zero-temperature correlation functions is obtained in the thermodynamic limit.
We present a review of the method we have elaborated to compute the correlation functions of the XXZXXZXXZ spin-1/2 Heisenberg chain.This method is based on the resolution of the quantum inverse scattering problem in the algebraic Bethe Ansatz bamework, and leads to a mul- tiple integral representation of the dynamical correlation functions.We describe in particular some recent advances concerning the two-point functions: in the finite chain, they can be expressed in terms of a single multiple integral.Such a formula provides a direct analytic connection between the previously obtained multiple integral representations and the form factor expansions for the correlation functions.