Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields

TL;DR

This paper investigates the large-scale energy spectra of a quantum antiferromagnetic Ising chain with mixed fields, revealing non-universal intermediate scale behavior distinct from single-particle Anderson localization, using SVD-based spectral analysis.

Contribution

It introduces a global unfolding method using SVD to analyze the energy spectra of many-body localized systems, uncovering non-universal intermediate scale properties.

Findings

Spectra exhibit super Posissonian statistics at intermediate scales.

SVD-based unfolding reveals non-universal behavior distinct from Anderson localization.

Intermediate energy scales show unique spectral properties.

Abstract

In recent years it became clear that the metallic regime of systems that exhibit a many body localization (MBL) behavior show properties which are quite different than the vanilla metallic region of the single particle Anderson regime. Here we show that the large scale energy spectrum of a canonical microscopical model featuring MBL, displays a non-universal behavior at intermediate scales, which is distinct from the deviation from universality seen in the single particle Anderson regime. The crucial step in revealing this behavior is a global unfolding of the spectrum performed using the singular value decomposition (SVD) which takes into account the sample to sample fluctuations of the spectra. The spectrum properties may be observed directly in the singular value amplitudes via the scree plot, or by using the SVD to unfold the spectra and then perform a number of states variance calculation. Both methods reveal an intermediate scale of energies which follow super Posissonian statistics.