Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems

TL;DR

This paper studies a spatial subsystem entropy derived from the one-particle density matrix in disordered fermion systems, revealing localization features, area law behavior, and logarithmic growth over time, useful for diagnosing many-body localization.

Contribution

It introduces and analyzes the OPDM entropy as a new diagnostic tool for many-body localization, demonstrating its scaling properties and computational efficiency.

Findings

OPDM entropy obeys an area law in MBL phase

OPDM entropy grows logarithmically with time after a quench

Computational cost scales polynomially with system size

Abstract

We investigate a spatial subsystem entropy extracted from the one-particle density matrix (OPDM) in one-dimensional disordered interacting fermions that host a many-body localized (MBL) phase. Deep in the putative MBL regime, this OPDM entropy exhibits the salient features of localization, despite not being a proper entanglement measure. We numerically show that the OPDM entropy of the eigenstates obeys an area law. Similar to the von-Neumann entropy, the OPDM entropy grows logarithmically with time after a quantum quench, albeit with a different prefactor. Both these features survive at moderately large interactions and well towards the transition into the ergodic phase. The computational cost to calculate the OPDM entropy scales only polynomially with the system size, suggesting that the OPDM provides a promising starting point for developing diagnostic tools for MBL in simulations and experiments.