Free-fermion Page Curve: Canonical Typicality and Dynamical Emergence

TL;DR

This paper analytically investigates the free-fermion Page curve, revealing canonical typicality and atypicality, and demonstrates its emergence in simple models, providing insights into quantum thermalization beyond conventional paradigms.

Contribution

It offers new analytical understanding of the free-fermion Page curve, highlighting differences from interacting systems and showing its emergence in simple models.

Findings

Canonical typicality is weaker in free-fermion systems.

The free-fermion Page curve differs significantly for large subsystems.

The Page curve emerges accurately in long-time quench dynamics of simple models.

Abstract

We provide further analytical insights into the newly established noninteracting (free-fermion) Page curve, focusing on both the kinematic and dynamical aspects. First, we unveil the underlying canonical typicality and atypicality for random free-fermion states. The former appears for a small subsystem and is exponentially weaker than the well-known result in the interacting case. The latter explains why the free-fermion Page curve differs remarkably from the interacting one when the subsystem is macroscopically large, i.e., comparable with the entire system. Second, we find that the free-fermion Page curve emerges with unexpectedly high accuracy in some simple tight binding models in long-time quench dynamics. This contributes a rare analytical result concerning quantum thermalization on a macroscopic scale, where conventional paradigms such as the generalized Gibbs ensemble and quasi-particle picture are not applicable.