# Origin of Temperature Gradient in Nonequilibrium Steady States in Weakly Coupled Quantum Spin Systems

## TL;DR

This paper develops an analytical perturbation theory to understand the origin of temperature gradients in nonequilibrium steady states of weakly coupled quantum spin chains, revealing conditions for nonzero temperature gradients independent of system integrability.

## Contribution

It introduces a perturbation approach for weakly coupled quantum spin systems to analytically determine the conditions for temperature gradients in NESSs.

## Key findings

- Derived a simple, integrability-independent condition for nonzero temperature gradients.
- Established an analytical framework for NESSs in weakly coupled quantum spin chains.
- Demonstrated the applicability of the theory to various quantum spin models.

## Abstract

We study nonequilibrium steady states (NESSs) in quantum spin-1/2 chains in contact with two heat baths at different temperatures. We consider the weak-coupling limit both for spin-spin coupling in the system and for system-bath coupling. This setting allows us to treat NESSs with a nonzero temperature gradient analytically. We develop a perturbation theory for this weak-coupling situation and show a simple condition for the existence of nonzero temperature gradient. This condition is independent of the integrability of the system.