Prerelaxation in quantum, classical, and quantum-classical two-impurity models

TL;DR

This study investigates the phenomenon of prerelaxation or metastability in impurity-host systems across quantum, classical, and hybrid models, revealing conditions under which impurities remain excited longer than expected due to various mechanisms.

Contribution

It provides a comparative numerical analysis of prerelaxation phenomena in three different impurity models, identifying mechanisms behind metastability.

Findings

Metastability occurs in next-nearest-neighbor impurity configurations.

Different models exhibit similar qualitative relaxation behavior.

Mechanisms include bound states, conserved observables, and cancellation effects.

Abstract

We numerically study the relaxation dynamics of impurity-host systems, focusing on the presence of long-lived metastable states in the non-equilibrium dynamics after an initial excitation of the impurities. In generic systems, an excited impurity coupled to a large bath at zero temperature is expected to relax and approach its ground state over time. However, certain exceptional cases exhibit metastability, where the system remains in an excited state on timescales largely exceeding the typical relaxation time. We study this phenomenon for three prototypical impurity models: a tight-binding quantum model of independent spinless fermions on a lattice with two stub impurities, a classical-spin Heisenberg model with two weakly coupled classical impurity spins, and a tight-binding quantum model of independent electrons with two classical impurity spins. Through numerical integration of the fundamental equations of motion, we find that all three models exhibit similar qualitative behavior: complete relaxation for nearest-neighbor impurities and incomplete or strongly delayed relaxation for next-nearest-neighbor impurities. The underlying mechanisms leading to this behavior differ between models and include impurity-induced bound states, emergent approximately conserved local observables, and exact cancellation of local and nonlocal dissipation effects.