Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems

TL;DR

This paper explores how entanglement entropy laws in free fermion systems relate to eigenstate thermalization, showing that typical excited states exhibit thermal properties due to entanglement, thus illustrating the emergence of statistical physics from quantum states.

Contribution

It reveals a duality linking entanglement entropy laws and introduces eigenstate typicality, demonstrating thermalization in free fermion systems from a single eigenstate.

Findings

Entanglement entropy area law and volume law are related by position-momentum duality.

Typical excited states exhibit eigenstate typicality, approaching thermal density matrices.

Eigenstate typicality explains how statistical physics emerges from quantum eigenstates.

Abstract

We demonstrate that the entanglement entropy area law for free fermion ground states and the corresponding volume law for highly excited states are related by a position-momentum duality, thus of the same origin. For a typical excited state in the thermodynamic limit, we further show that the reduced density matrix of a subsystem approaches thermal density matrix, provided the subsystem's linear size is small compared to that of the whole system in all directions, a property we dub eigenstate typicality. This provides an explicit example of thermalization via entanglement, and reveals how statistical physics emerges from a single eigenstate by tracing out a large number of degrees of freedom.