Beyond the Lindblad Master Equation: Heat, Work and Energy Currents in Boundary Driven Spin Chains

TL;DR

This paper investigates energy, heat, and work currents in boundary-driven quantum spin chains using a repeated interaction scheme, revealing cases where traditional Lindblad equations are insufficient for describing heat in such systems.

Contribution

It introduces a method to accurately compute energy, heat, and work currents beyond Lindblad equations using a repeated interaction approach for boundary-driven quantum spin chains.

Findings

Identifies cases where heat and work currents contribute to the same energy current.

Shows that Lindblad master equations may not fully capture heat in boundary-driven quantum systems.

Provides analytical steady-state distributions for small systems.

Abstract

We consider the accurate investigation of the energy current and its components, heat and work, in some boundary driven quantum spin systems. The expressions for the currents, as well as the associated Lindblad master equation, are obtained via a repeated interaction scheme. We consider small systems in order to analytically compute the steady distribution to study the current in the steady state. Asymmetrical XXZ and quantum Ising models are detailed analyzed. For the XXZ chain we present cases in which different compositions of heat and work currents, obtained via the repeated interaction protocol, lead to the same energy current, which may be obtained via the Lindblad master equation. For the quantum Ising chain, we describe a case of zero energy current and novanishing heat and work currents. Our findings make clear that to talk about heat in these boundary driven spin quantum systems we must go beyond an investigation involving only the Lindblad master equation.