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/9204011

Fredholm Determinant Representation for Correlation Functions in XXO Heisenberg Chain

Filippo Colomo, Anatoli G. Izergin, V. E. Korepin

Published Apr 22, 1992• 1 citation
arXivHTMLPDF

Abstract

Space and time dependent temepreture correlation fucntions in the Hiesenberg XXO chain are evaluated in the magnetic field. The other name of the model is isotropic xy model in the transverse magnetic field. In the thermodynamic limit correlations in the model are represented as Fredhom determinanat. We expect this to to solve the problem of evaluation of asymptotics of temperature correlations.

DOI
10.48550/arxiv.cond-mat/9204011

Related papers

Temperature Correlations of Quantum Spins

Alexandr Its, Anatloij Izergin, Vladimr Korepin +1 more

We consider isotropic XY model in the transverse magnetic field on the one dimensional lattice. Another name of the model in Heisenberg XXO model of spin 1/2.We solved long standing problem of evaluation of temperature correlations. We first represent correlation function in the model, by means of completely integrable differential equation. This is famous Ablowitz-Ladik lattice Nonlinear Schrodinger equation.Correlation function is the $τ$ function of this differential equation. We solved this equation and evaluate asymptotics.

arXiv:cond-mat/9209034•Sep 30, 1992•0 citations

Determinant Representation for time and temperature dependent correlation functions in the isotropic XY model in the transverse magnetic field

Filippo Colomo, Anatoli G. Izergin, V. E. Korepin +1 more

Astymptotics of temperature correlations is the most dificult problem of stat. mech. Recently it was solved for the impenetrable Bose Gas. The idea is to represent correlation function as $τ$ function of calssical completely integrable differential equation. Now we start to apply this program to isotropic XY model in the trasnsverse magnetic field. In this paper we are making first step. We representing correlation function as detrminanat of an integral operator.

arXiv:cond-mat/9205009•May 16, 1992•1 citation

Temperature correlations of quantum spins

Alexander Rudol'fovich Its, Anatoli G. Izergin, V. E. Korepin +1 more

We consider the isotropic XY model in a transverse magnetic field in one dimension. One can alternatively call this model the Heisenberg XXO antiferromagnet. We solve the problem of the evaluation of asymptotics of temperature correlations and explain the physical meaning of our result. To do this we represent the quantum correlation function as a tau function of a completely integrable differential equation. This is the well-known Ablowitz-Ladik lattice nonlinear Schr\"odinger differential equation.

arXiv:hep-th/9212135•Physical Review Letters•Mar 15, 1993•131 citations

The large time asymptotics of the temperature correlation functions of the XXO Heisenberg ferromagnetic: The Reimann-Hilbert approach

Xiaojun Jie

The finite temperature correlation functions of the time-dependent local spin operators of the Heisenberg XXO ferromagnet are considered. The Fredholm determinant representation for these correlation functions were obtained in 1992 by Colomo, Izergin, Korepin, and Tognetti. The problem addressed in this dissertation consists of the asymptotic analysis of the XXO correlation functions based on the determinant representations mentioned. The integral kernel involved in the Colomo-Izergin-Korepin-Tognetti determinant representations belongs to the class of “integrable kernels” which usually appear in the theory of exactly solvable statistical mechanics models, and also in the theory of random matrices. This makes it possible to analyze the large time behavior of the correlation functions in the framework of the Riemann-Hilbert approach. In the dissertation, the associated matrix Riemann-Hilbert problem is solved asymptotically via properly modified Deift-Zhou nonlinear steepest descent method. This in turn allows us to determine the structure of the long-time asymptotic series for the correlation functions and to evaluate explicitly the exponential, power-like pre-exponential, and the oscillatory factors of the asymptotics. A recursive procedure for evaluation of the corrections of any order, which is based on the relevant zero-curvature equation, is suggested as well.

•Jan 1, 1998•0 citations

Dynamical correlation functions of theXXZmodel at finite temperature

Kazumitsu Sakai

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.

arXiv:cond-mat/0703319•Journal of Physics A Mathematical and Theoretical•Jun 19, 2007•34 citations

Time-dependent correlation functions in the high-temperature limit for the XY-chain and the Ising-chain in a transverse magnetic field

Jacques H. H. Perk, Hans W. Capel

Some exact results are presented for the time correlations between x- and y- components of spins (S=1/2) and their frequency-Fourier transforms in the one-dimensional XY-model in the high-temperature limit (β=0). The results show a predominantly Gaussian decay.

Journal of Applied Physics•Mar 1, 1979•2 citations
Space and time dependent temepreture correlation fucntions in the Hiesenberg XXO chain are evaluated in the magnetic field. The other name of the model is isotropic xy model in the transverse magnetic field. In the thermodynamic limit correlations in the model are represented as Fredhom determinanat. We expect this to to solve the problem of evaluation of asymptotics of temperature correlations.
We consider isotropic XY model in the transverse magnetic field on the one dimensional lattice. Another name of the model in Heisenberg XXO model of spin 1/2.We solved long standing problem of evaluation of temperature correlations. We first represent correlation function in the model, by means of completely integrable differential equation. This is famous Ablowitz-Ladik lattice Nonlinear Schrodinger equation.Correlation function is the τττ function of this differential equation. We solved this equation and evaluate asymptotics.
Astymptotics of temperature correlations is the most dificult problem of stat. mech. Recently it was solved for the impenetrable Bose Gas. The idea is to represent correlation function as τττ function of calssical completely integrable differential equation. Now we start to apply this program to isotropic XY model in the trasnsverse magnetic field. In this paper we are making first step. We representing correlation function as detrminanat of an integral operator.
We consider the isotropic XY model in a transverse magnetic field in one dimension. One can alternatively call this model the Heisenberg XXO antiferromagnet. We solve the problem of the evaluation of asymptotics of temperature correlations and explain the physical meaning of our result. To do this we represent the quantum correlation function as a tau function of a completely integrable differential equation. This is the well-known Ablowitz-Ladik lattice nonlinear Schr\"odinger differential equation.
The finite temperature correlation functions of the time-dependent local spin operators of the Heisenberg XXO ferromagnet are considered. The Fredholm determinant representation for these correlation functions were obtained in 1992 by Colomo, Izergin, Korepin, and Tognetti. The problem addressed in this dissertation consists of the asymptotic analysis of the XXO correlation functions based on the determinant representations mentioned. The integral kernel involved in the Colomo-Izergin-Korepin-Tognetti determinant representations belongs to the class of “integrable kernels” which usually appear in the theory of exactly solvable statistical mechanics models, and also in the theory of random matrices. This makes it possible to analyze the large time behavior of the correlation functions in the framework of the Riemann-Hilbert approach. In the dissertation, the associated matrix Riemann-Hilbert problem is solved asymptotically via properly modified Deift-Zhou nonlinear steepest descent method. This in turn allows us to determine the structure of the long-time asymptotic series for the correlation functions and to evaluate explicitly the exponential, power-like pre-exponential, and the oscillatory factors of the asymptotics. A recursive procedure for evaluation of the corrections of any order, which is based on the relevant zero-curvature equation, is suggested as well.