Temperature Correlations of Quantum Spins

TL;DR

This paper solves a long-standing problem by deriving and solving a differential equation for temperature correlations in the 1D XY spin model, revealing asymptotic behaviors of the correlation functions.

Contribution

It introduces a novel approach by representing the correlation function as a tau function of an integrable differential equation, specifically the Ablowitz-Ladik lattice.

Findings

Derived an explicit representation of temperature correlations

Solved the associated Ablowitz-Ladik nonlinear Schrödinger equation

Provided asymptotic analysis of the correlation functions

Abstract

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 $\tau $ function of this differential equation. We solved this equation and evaluate asymptotics.