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Eigenstate correlations around the many-body localization transition

Tikhonov, K. S.; Mirlin, A. D.

Abstract (englisch):
We explore correlations of eigenstates around the many-body localization (MBL) transition in their de-pendence on the energy difference (frequency)ωand disorderW. In addition to the genuine many-bodyproblem, XXZ spin chain in random field, we consider localization on random regular graphs that servesas a toy model of the MBL transition. Both models show a very similar behavior. On the localized side ofthe transition, the eigenstate correlation functionβ(ω) shows a power-law enhancement of correlations withloweringω; the corresponding exponent depends onW. The correlation between adjacent-in-energy eigenstatesexhibits a maximum at the transition pointWc, visualizing the drift ofWcwith increasing system size towardsits thermodynamic-limit value. The correlation functionβ(ω) is related, via Fourier transformation, to theHilbert-space return probability. We discuss measurement of such (and related) eigenstate correlation functionson state-of-the-art quantum computers and simulators.

DOI: 10.1103/PhysRevB.103.064204
Zitationen: 8
Zugehörige Institution(en) am KIT Institut für Quantenmaterialien und -technologien (IQMT)
Institut für Theorie der Kondensierten Materie (TKM)
Publikationstyp Zeitschriftenaufsatz
Publikationsdatum 15.02.2021
Sprache Englisch
Identifikator ISSN: 2469-9950, 2469-9969
KITopen-ID: 1000129942
HGF-Programm 47.12.01 (POF IV, LK 01) Advanced Solid-State Qubits and Qubit Systems
Erschienen in Physical review / B
Verlag American Physical Society (APS)
Band 103
Heft 6
Seiten Article: 064204
Vorab online veröffentlicht am 12.02.2021
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