Characterizing correlations with full counting statistics: classical Ising and quantum XY spin chains

TL;DR

This paper introduces a method to analyze correlations in classical and quantum spin chains using full counting statistics, successfully applied to the Ising and XY models to identify phase diagrams and phases.

Contribution

It presents a novel approach employing full counting statistics to characterize correlations and phase diagrams in classical and quantum spin chains.

Findings

Identified phase boundaries in the classical Ising model.

Reproduced known phase diagram of the quantum XY chain.

Distinguished phases via long-distance behavior of Jordan-Wigner strings.

Abstract

We propose to describe correlations in classical and quantum systems in terms of full counting statistics of a suitably chosen discrete observable. The method is illustrated with two exactly solvable examples: the classical one-dimensional Ising model and the quantum spin-1/2 XY chain. For the one-dimensional Ising model, our method results in a phase diagram with two phases distinguishable by the long-distance behavior of the Jordan-Wigner strings. For the quantum XY chain, the method reproduces the previously known phase diagram.