Grand Canonical-like Thermalization of Quantum Many-body Scars

TL;DR

This paper introduces a new framework for understanding quantum many-body scars by developing an effective open-system description, defining quasiparticle number, and formulating a revised ETH that explains anomalous fluctuations and dynamics.

Contribution

It presents a novel effective open-system approach and a revised ETH incorporating quasiparticle number, providing a unified understanding of QMBS and thermalization in constrained systems.

Findings

Revised ETH accurately predicts long-time averages of local observables.

Introduces cross coherence purity (CCP) as a measure of off-diagonal matrix elements.

Explains anomalous fluctuations and quasi-periodic dynamics of scar states.

Abstract

Quantum many-body scar (QMBS) in kinetically constrained quantum systems challenges the conventional eigenstate thermalization hypothesis (ETH). We develop an effective open-system description for constrained dynamics and introduce the definition of quasiparticle number in the system. Based on this, we formulate a revised ETH that accounts for both diagonal and off-diagonal structures of local observables. By introducing the cross coherence purity (CCP), we obtain a unified characterization of off-diagonal matrix elements and show that the relevant density of states (DOS) is determined by the distribution of eigenstates on the energy--quasiparticle-number plane. We numerically verify an inverse relation between the CCP and this generalized DOS. Applied to the quantum many-body scar model, the revised ETH accurately predicts long-time averages and temporal fluctuations of local observables and explains their dependence on initial states. Our framework shows that the anomalous fluctuations and quasi-periodic dynamics of scar states arise naturally from low-DOS regions. These results provide a unified understanding of thermalization and QMBS in kinetically constrained systems.