Fluctuations of the heat exchanged between two quantum spin chains

TL;DR

This paper investigates the heat exchange statistics between two quantum XX spin chains at different temperatures, deriving formulas for average heat and distribution, and revealing sensitivity to quantum phase transitions.

Contribution

It provides new analytical formulas for heat exchange statistics in quantum spin chains, applicable to arbitrary sizes and highlighting the impact of quantum phase transitions.

Findings

Heat exchange statistics are sensitive to quantum phase transitions.

Derived formulas are valid for chains of any size.

Thermodynamic quantities show critical behavior near phase transitions.

Abstract

The statistics of the heat exchanged between two quantum XX spin chains prepared at different temperatures is studied within the assumption of weak coupling. This provides simple formulas for the average heat and its corresponding characteristic function, from which the probability distribu- tion may be computed numerically. These formulas are valid for arbitrary sizes and therefore allow us to analyze the role of the thermodynamic limit in this non-equilibrium setting. It is found that all thermodynamic quantities are extremely sensitive to the quantum phase transition of the XX chain.