Decay of transverse correlations in quantum Heisenberg models

TL;DR

This paper proves that in certain quantum spin systems, including Heisenberg and XY models, two-point correlations decay exponentially when a transverse magnetic field, possibly random, is applied, using probabilistic methods.

Contribution

It introduces a probabilistic proof of exponential decay of correlations in quantum Heisenberg models with random transverse fields, extending previous results.

Findings

Exponential decay of correlations in specified quantum models.

Applicability to models with random transverse magnetic fields.

Use of probabilistic and percolation techniques in quantum spin systems.

Abstract

We study a class of quantum spin systems that includes the $S=\tfrac12$ Heisenberg and XY-models, and prove that two-point correlations exhibit exponential decay in the presence of a transverse magnetic field. The field is not necessarily constant, it may be random, and it points in the same direction. Our proof is entirely probabilistic and it relies on a random-loop-representation of the correlation functions, on stochastic domination, and on first-passage percolation.