High temperature expansion of emptiness formation probability for isotropic Heisenberg chain

TL;DR

This paper develops a high temperature expansion method for calculating the emptiness formation probability in the isotropic Heisenberg chain, achieving high-order accuracy and validating results with Quantum Monte Carlo simulations.

Contribution

It introduces a systematic high temperature expansion for the emptiness formation probability in the Heisenberg chain, extending to high orders and confirming accuracy through numerical comparisons.

Findings

High order HTE formulas for P(n) up to O((J/T)^42) for n=3.

Excellent agreement between HTE results and Quantum Monte Carlo data.

Effective application of HTE to finite temperature correlation functions.

Abstract

Recently, G\"ohmann, Kl\"umper and Seel have derived novel integral formulas for the correlation functions of the spin-1/2 Heisenberg chain at finite temperature. We have found that the high temperature expansion (HTE) technique can be effectively applied to evaluate these integral formulas. Actually, as for the emptiness formation probability ${P(n)}$ of the isotropic Heisenberg chain, we have found a general formula of the HTE for ${P(n)}$ with arbitrary $n \in {\mathbb Z}_{\ge 2}$ up to ${O((J/T)^{4})}$. If we fix a magnetic field to a certain value, we can calculate the HTE to much higher order. For example, the order up to ${O((J/T)^{42})}$ has been achieved in the case of ${P(3)}$ when ${h=0}$. We have compared these HTE results with the data by Quantum Monte Carlo simulations. They exhibit excellent agreements.