Quantum master equation for many-body systems: Derivation based on the Lieb-Robinson bound

TL;DR

This paper derives a local quantum master equation for many-body systems using the Lieb-Robinson bound, clarifying its microscopic validity and testing it numerically on a fermion chain.

Contribution

The authors provide a derivation of the local GKSL quantum master equation based on the Lieb-Robinson bound, expanding its applicability to broader many-body systems.

Findings

Derived the local GKSL equation from the Lieb-Robinson bound.

Numerically validated the equation for a 1D fermion chain.

Clarified conditions for the equation's validity in many-body systems.

Abstract

The local Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) quantum master equation is a powerful tool for the study of open quantum many-body systems. However, its microscopic derivation applicable to many-body systems is available only in limited cases of weak internal couplings, and it has yet to be fully understood under what microscopic conditions the local GKSL equation is valid. We derive the local GKSL equation on the basis of the Lieb-Robinson bound, which provides an upper bound of the propagation of information in quantum many-body systems. We numerically test the validity of the derived local GKSL equation for a one-dimensional tight-binding fermion chain.