Fock-space geometry and strong correlations in many-body localized systems

TL;DR

This paper uses a geometric approach to analyze Fock space in many-body localized systems, revealing how eigenstates resemble Slater determinants and exhibit complex correlations and incompatibilities across different states and regimes.

Contribution

It introduces a geometric framework to quantify state incompatibility and correlations in many-body localized systems, providing new insights into quasiparticle excitations.

Findings

Eigenstates are well approximated by Slater determinants.

Incompatibility between states varies and is quantifiable.

Strong correlations exist between states of different particle numbers.

Abstract

We adopt a geometric perspective on Fock space to provide two complementary insights into the eigenstates in many-body-localized fermionic systems. On the one hand, individual many-bodylocalized eigenstates are well approximated by a Slater determinant of single-particle orbitals. On the other hand, the orbitals of different eigenstates in a given system display a varying, and generally imperfect, degree of compatibility, as we quantify by a measure based on the projectors onto the corresponding single-particle subspaces. We study this incompatibility between states of fixed and differing particle number, as well as inside and outside the many-body-localized regime. This gives detailed insights into the emergence and strongly correlated nature of quasiparticle-like excitations in many-body localized systems, revealing intricate correlations between states of different particle number down to the level of individual realizations.