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

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.

11 pages, 10 figures

References in corpus (17)

• Anderson Transitions
• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Spectral signatures of many-body localization with interacting photons
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Ergodicity breaking in a model showing many-body localization
• Anomalous thermalization in ergodic systems
• Non-ergodic phases in strongly disordered random regular graphs
• Extended nonergodic states in disordered many-body quantum systems
• Renormalization-group study of the many-body localization transition in one dimension
• Critical behavior at the localization transition on random regular graphs
• Many-body localization near the critical point
• Probing the metallic energy spectrum beyond the Thouless energy scale using the singular value decomposition
• Reentrant Random Quantum Ising Antiferromagnet

Cited by in corpus (5)

• Sachdev-Ye-Kitaev model: Non-self-averaging properties of the energy spectrum
• Unification of Finite Symmetries in Simulation of Many-body Systems on Quantum Computers
• Random Ising chain in transverse and longitudinal fields: Strong disorder RG study
• Unfolding a composed ensemble of energy spectra using singular value decomposition
• A Complex Network Analysis on The Eigenvalue Spectra of Random Spin Systems