The Smearing of Quasi-Particles: Signatures in the Entanglement Entropy of Excited Many-Particle Systems

TL;DR

This paper investigates how quasi-particles influence the entanglement entropy in excited many-body quantum systems, revealing a linear energy dependence linked to quasi-particle properties and its breakdown at high energies or strong interactions.

Contribution

It introduces a theoretical and numerical analysis of the crossover in entanglement entropy scaling driven by quasi-particles in various many-body models.

Findings

Linear EE dependence on energy indicates quasi-particle presence.

Breakdown of linearity at high energy and strong interactions.

Qp weight decreases with increasing interaction strength.

Abstract

The entanglement spectrum serves as a powerful tool for probing the structure and dynamics of quantum many-body systems, revealing key information about symmetry, topology, and excitations. While the entanglement entropy (EE) of ground states typically follows an area law, highly excited states obey a volume law, leading to a striking contrast in their scaling behavior. In this paper, we investigate the crossover between these two regimes, focusing on the role of quasi-particles (QPs) in mediating this transition. By analyzing the energy dependence of EE in various many-body systems, we explore how the presence of long-lived QPs influences the entanglement structure of excited states. We present numerical results for spinless fermions, a spin chain near a many-body localization transition, and the Sachdev-Ye-Kitaev (SYK) model, which lacks a conventional QP description. Our findings are complemented by a theoretical model based on Fermi liquid theory, providing insight into the interaction-dependent scaling of EE and its consistency with numerical simulations. We find that a hallmark of QPs is a linear dependence of the eigenstate EE on energy, which breaks down at high energy and in the limit of strong interaction. The slope of this linear dependence reflects the QP weight, which reduces with interaction strength.