Fermionic magic resources in disordered quantum spin chains

TL;DR

This paper investigates how fermionic non-Gaussianity, measured by antiflatness, varies across ergodic and many-body localized regimes in disordered quantum spin chains, revealing its potential as a diagnostic tool for MBL and ergodicity.

Contribution

It introduces fermionic antiflatness as a measure of non-Gaussianity in disordered spin chains and explores its behavior in different regimes, highlighting its diagnostic power.

Findings

FAF decreases in MBL regime, showing area-law scaling

FAF is enhanced in rare eigenstates, indicating destabilization mechanisms

FAF grows slowly over time in MBL, approaching saturation

Abstract

Fermionic non-Gaussianity quantifies a quantum state's deviation from a classically tractable free-fermionic description, constituting a necessary resource for computational quantum advantage. Here we use fermionic antiflatness (FAF) to measure this deviation across ergodic and many-body localized (MBL) regimes. We focus on the paradigmatic disordered spin-$1\!/2$ XXZ chain and its impurity variant with local interactions. Across highly excited eigenstates, FAF evolves from typical-state behavior at weak disorder to strongly suppressed values deep in the MBL regime, with volume-law scaling in the XXZ chain and an area-law bound in the impurity setting. Rare long range catlike eigenstates exhibit a pronounced enhancement of FAF, making it a sensitive diagnostic of mechanisms proposed to destabilize MBL. Starting from product states, we find that in the MBL regime FAF grows slowly in time, approaching saturation via a power-law relaxation. Overall, our results show that MBL suppresses fermionic non-Gaussianity, and the associated complexity beyond free fermions, while ergodicity restores it, motivating explorations of fermionic non-Gaussianity in other ergodicity-breaking phenomena.