Analysis of Many-body Localization Landscapes and Fock Space Morphology via Persistent Homology

TL;DR

This paper employs persistent homology, an algebraic topology tool, to analyze many-body localization landscapes and Fock space structures, revealing new insights into eigenstate distributions and phase transitions.

Contribution

It introduces novel persistent homology observables for many-body localization, providing a new topological perspective on eigenstate structure near the critical point.

Findings

Persistent homology observables show transitional behavior near the critical point.

The approach offers insights into eigenstate structure beyond traditional methods.

New tools for analyzing Fock space landscapes in many-body systems.

Abstract

We analyze functionals that characterize the distribution of eigenstates in Fock space through a tool derived from algebraic topology: persistent homology. Drawing on recent generalizations of the localization landscape applicable to mid-spectrum eigenstates, we introduce several novel persistent homology observables in the context of many-body localization that exhibit transitional behavior near the critical point. We demonstrate that the persistent homology approach to localization landscapes and, in general, functionals on the Fock space lattice offer insights into the structure of eigenstates unobtainable by traditional means.