The Ising Limit of the XXZ Heisenberg Magnet and Certain Thermal Correlation Functions

TL;DR

This paper investigates the Ising limit of the XXZ Heisenberg magnet, deriving thermal correlation functions using symmetric Schur functions, and finds a connection to plane partitions at low temperatures.

Contribution

It introduces a novel approach to calculating correlation functions in the Ising limit using symmetric Schur functions and links the amplitude to plane partitions.

Findings

Correlation functions expressed via symmetric Schur functions.

Amplitude proportional to squared numbers of strict boxed plane partitions.

Low-temperature asymptotics characterized by these combinatorial structures.

Abstract

The spin-1/2 XXZ Heisenberg magnet is considered for the case of the anisotropy parameter tending to infinity (so-called, Ising limit). A thermal correlation function of the ferromagnetic string is calculated over the ground state. The approach to the calculation of the correlation functions in the limit of infinite anisotropy is based on the observation that the wave function is expressed in terms of the symmetric Schur functions. It is demonstrated that at low temperatures the amplitude of the asymptotical expression of this correlation function is proportional to the squared numbers of strict boxed plane partitions.