Eigenstate correlations around the many-body localization transition
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.
- Publication:
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Physical Review B
- Pub Date:
- February 2021
- DOI:
- 10.1103/PhysRevB.103.064204
- arXiv:
- arXiv:2009.09685
- Bibcode:
- 2021PhRvB.103f4204T
- Keywords:
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- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- Phys. Rev. B 103, 064204 (2021)