Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure

TL;DR

This paper studies how weak to moderate perturbations with a banded matrix structure affect the relaxation dynamics of isolated quantum many-body systems, providing analytical and numerical insights.

Contribution

It introduces a nonperturbative framework linking perturbation profiles to relaxation modifications, with analytical solutions and numerical validation for banded matrix structures.

Findings

Analytical solutions match numerical results for weak and strong perturbations.

Banded matrix structures significantly influence relaxation behavior.

Numerical simulations confirm theoretical predictions without free parameters.

Abstract

We investigate how the observable relaxation behavior of an isolated quantum many-body system is modified in response to weak-to-moderate perturbations within a nonperturbative typicality framework. A key role is played by the so-called perturbation profile, which characterizes the dependence of the perturbation matrix elements in the eigenbasis of the unperturbed Hamiltonian on the difference of the corresponding energy eigenvalues. In particular, a banded matrix structure is quantitatively captured by a perturbation profile which approaches zero for large energy differences. The temporal modification of the relaxation is linked to the perturbation profile via a nonlinear integral equation, which admits approximate analytical solutions for sufficiently weak and strong perturbations, and for which we work out a numerical solution scheme in the general case. As an example, we consider a spin lattice model with a pronounced banded matrix structure, and we find very good agreement of the numerics with our analytical predictions without any free fit parameter.