Nontrivial damping of quantum many-body dynamics

TL;DR

This paper investigates how quantum many-body systems exhibit nontrivial damping behaviors under perturbations, especially when interactions lead to complex dynamics, challenging the typical exponential damping predictions.

Contribution

It introduces a framework showing that rich unperturbed dynamics can cause nontrivial damping in the Schrödinger picture, supported by large-scale numerical simulations.

Findings

Nontrivial damping can emerge from complex unperturbed dynamics.

Exponential damping is not universal and depends on system features.

Numerical simulations confirm theoretical predictions in Fermi-Hubbard chains.

Abstract

Understanding how the dynamics of a given quantum system with many degrees of freedom is altered by the presence of a generic perturbation is a notoriously difficult question. Recent works predict that, in the overwhelming majority of cases, the unperturbed dynamics is just damped by a simple function, e.g., exponentially as expected from Fermi's golden rule. While these predictions rely on random-matrix arguments and typicality, they can only be verified for a specific physical situation by comparing to the actual solution or measurement. Crucially, it also remains unclear how frequent and under which conditions counterexamples to the typical behavior occur. In this work, we discuss this question from the perspective of projection-operator techniques, where exponential damping of a density matrix occurs in the interaction picture but not necessarily in the Schr\"odinger picture. We show that a nontrivial damping in the Schr\"odinger picture can emerge if the dynamics in the unperturbed system possesses rich features, for instance due to the presence of strong interactions. This suggestion has consequences for the time dependence of correlation functions. We substantiate our theoretical arguments by large-scale numerical simulations of charge transport in the extended Fermi-Hubbard chain, where the nearest-neighbor interactions are treated as a perturbation to the integrable reference system.