Heat rectification on the XX chain

TL;DR

This paper investigates thermal rectification in a simple quantum spin chain, demonstrating that rectification can persist in large systems and is a general feature of quantum spin models.

Contribution

It provides a rigorous analysis of heat rectification in the open XX chain using Lindblad dynamics, showing rectification persists in the thermodynamic limit.

Findings

Thermal rectification occurs even in slightly asymmetrical chains.

Rectification remains finite as system size increases.

Rectification is a general phenomenon in quantum spin systems.

Abstract

In order to better understand the minimal ingredients for thermal rectification, we perform a detailed investigation of a simple spin chain, namely, the open XX model with a Lindblad dynamics involving global dissipators. We use a Jordan-Wigner transformation to derive a mathematical formalism to compute the heat currents and other properties of the steady state. We have rigorous results to prove the occurrence of thermal rectification even for slightly asymmetrical chains. Interestingly, we describe cases where the rectification does not decay to zero as we increase the system size, that is, the rectification remains finite in the thermodynamic limit. We also describe some numerical results for more asymmetrical chains. The presence of thermal rectification in this simple model indicates that the phenomenon is of general occurrence in quantum spin systems.