Eigenstate correlations around the many-body localization transition

K. S. Tikhonov, A. D. Mirlin

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

We explore correlations of eigenstates around the many-body localization (MBL) transition in their dependence on the energy difference (frequency) ω and disorder W. In addition to the genuine many-body problem, XXZ spin chain in random field, we consider localization on random regular graphs that serves as a toy model of the MBL transition. Both models show a very similar behavior. On the localized side of the transition, the eigenstate correlation function β(ω) shows a power-law enhancement of correlations with lowering ω; the corresponding exponent depends on W. The correlation between adjacent-in-energy eigenstates exhibits a maximum at the transition point Wc, visualizing the drift of Wc with increasing system size towards its thermodynamic-limit value. The correlation function β(ω) is related, via Fourier transformation, to the Hilbert-space return probability. We discuss measurement of such (and related) eigenstate correlation functions on state-of-the-art quantum computers and simulators.

Original languageEnglish
Article number064204
JournalPhysical Review B
Volume103
Issue number6
DOIs
Publication statusPublished - 12 Feb 2021

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