Derivation of Lindblad master equation for the quantum Ising model interacting with a heat bath

TL;DR

This paper derives a Lindblad master equation for the 1D quantum Ising model interacting with a heat bath, showing the steady state is a canonical distribution regardless of dissipation rate.

Contribution

It provides a rigorous derivation of the Lindblad equation for the quantum Ising model under weak coupling and Markov approximations, including proof of the steady state.

Findings

Steady state is the canonical distribution independent of dissipation rate

Derived Lindblad equation from first principles for the quantum Ising model

Validated the Markov and rotating wave approximations in this context

Abstract

Starting from the Liouville-von Neumann equation, under a weak coupling limit we derive the Lindblad master equation for the one-dimensional quantum Ising model in a Markov approximation and a rotating wave approximation. We also prove that the steady solution of the Lindblad equation is the canonical distribution independent of the dissipation rate.