Thermalization in open many-body systems and KMS detailed balance

TL;DR

This paper derives a first-principles quantum master equation for many-body systems that satisfies KMS detailed balance without relying on the rotating wave approximation, enabling accurate modeling of thermalization.

Contribution

It introduces a new quantum master equation that accounts for many-body interactions and satisfies KMS detailed balance, improving upon previous models.

Findings

Reproduces thermal equilibrium with small Hamiltonian renormalization.

Approximates true system evolution with linear-in-time error.

Can be efficiently simulated on quantum computers.

Abstract

Starting from a microscopic description of weak system-bath interactions, we derive from first principles a quantum master equation that does not rely on the well-known rotating wave approximation. This includes generic many-body systems, with Hamiltonians with vanishingly small energy spacings that forbid that approximation. The equation satisfies a general form of detailed balance, called KMS, which ensures exact convergence to the many-body Gibbs state. Unlike the more common notion of GNS detailed balance, this notion is compatible with the absence of the rotating wave approximation. We show that the resulting Lindbladian dynamics not only reproduces the thermal equilibrium point up to a small renormalization of the system Hamiltonian, but it also approximates the true system evolution with an error that grows at most linearly in time, giving an exponential improvement upon previous estimates. This master equation has quasi-local jump operators, can be efficiently simulated on a quantum computer, and reduces to the usual Davies dynamics in the limit of a coarse-graining time much larger than the inverse of the smallest frequency difference. With it, we provide a rigorous model of many-body thermalization relevant to both open quantum systems and quantum algorithms.