Integrals of motion as slow modes in dissipative many-body operator dynamics

TL;DR

This paper shows that integrals of motion in many-body quantum systems become slow-decaying modes under weak dissipation, linking their properties to the eigenoperators of the Lindbladian and offering a new way to identify IOMs.

Contribution

It introduces a novel connection between integrals of motion and slow modes in dissipative quantum dynamics, supported by numerical and perturbative evidence.

Findings

IOMs with small support decay more slowly under dissipation

Eigenoperators with slowest decay overlap significantly with IOMs

Provides a new method for identifying integrals of motion

Abstract

We consider Lindbladian operator dynamics in many-body quantum systems with one or more integrals of motion (IOM), subject to weak local dissipation. We demonstrate that IOMs with small support become slow modes of these dynamics, in the sense that their Frobenius norm decays more slowly compared to generic operators. As a result, the eigenoperators of such Lindbladians with slowest decay rates have a large overlap with the IOMs of the underlying Hamiltonian. We demonstrate this correspondence between slow modes and IOMs numerically for a number of many-body models, and further corroborate it with perturbative arguments. These results open up a new method for the identification of IOMs, and provide insights into the dissipative many-body dynamics.