A Path Integration Approach to the Correlators of XY Heisenberg Magnet and Random Walks

TL;DR

This paper employs a path integral method to compute correlation functions in the XY Heisenberg chain, revealing determinantal formulas linked to random walk models, enhancing understanding of quantum spin systems.

Contribution

It introduces a path integral framework for calculating XY magnet correlators and connects them to vicious walker generating functions, offering a novel analytical perspective.

Findings

Correlation functions are expressed in determinantal form.

Two-point correlators relate to vicious random walk generating functions.

Provides a new analytical tool for quantum spin chain analysis.

Abstract

The path integral approach is used for the calculation of the correlation functions of the $XY$ Heisenberg chain. The obtained answers for the two-point correlators of the $XX$ magnet are of the determinantal form and are interpreted in terms of the generating functions for the random turns vicious walkers.