Decay of Quantum Correlations in a Lattice by Heat Kernel Methods

TL;DR

This paper investigates how quantum correlations decay in lattice systems at high temperatures using heat kernel techniques, providing improved estimations for local observable correlations.

Contribution

It introduces an enhanced method for estimating quantum correlations in spin systems at large temperature by analyzing the heat kernel of the Hamiltonian.

Findings

Derived bounds for correlation decay at high temperature

Extended heat kernel analysis to infinite lattice dimensions

Improved previous estimations of quantum correlations

Abstract

We prove some estimations of the correlation of two local observables in quantum spin systems (with Schr\"odinger equations) at large temperature. For that, we describe the heat kernel of the Hamiltonian for a finite subset of the lattice, allowing the dimension to tend to infinity. This is an improved version of an earlier unpublished manuscript.