Large deviations in the many-body localization transition: The case of the random-field XXZ chain

Fuente: arXiv
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Main Authors: Miranda, Greivin Alfaro, Alet, Fabien, Biroli, Giulio, Cugliandolo, Leticia F., Laflorencie, Nicolas, Tarzia, Marco
Format: Preprint
Published: 2025
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author Miranda, Greivin Alfaro
Alet, Fabien
Biroli, Giulio
Cugliandolo, Leticia F.
Laflorencie, Nicolas
Tarzia, Marco
author_facet Miranda, Greivin Alfaro
Alet, Fabien
Biroli, Giulio
Cugliandolo, Leticia F.
Laflorencie, Nicolas
Tarzia, Marco
contents The effect of rare system-wide resonances in the many-body localization (MBL) transition has recently attracted significant attention. They are expected to play a prominent role in the stability of the MBL phase, prompting the development of new theoretical frameworks to properly account for their statistical weight. We employ a method based on an analogy with mean-field disordered glassy systems to characterize the statistics of transmission amplitudes between distant many-body configurations in Hilbert space, and apply it to the random-field XXZ spin chain. By introducing a Lagrange multiplier, which formally plays the role of an effective temperature controlling the influence of extreme outliers in the heavy-tailed distribution of propagators, we identify three distinct regimes: (i) an ergodic phase with uniform spreading in Hilbert space, (ii) an intermediate regime where delocalization is driven by rare, disorder-dependent long-range resonances, and (iii) a robust MBL phase where such resonances cannot destabilize localization. We derive a finite-size phase diagram in the disorder--interaction plane both in the spin and in the Anderson basis that quantitatively agrees with recent numerical results based on real-space spin-spin correlation functions. We further demonstrate that even infinitesimal interactions can destroy the Anderson insulator at finite disorder, with the critical disorder remaining finite down to small interaction strengths. By visualizing resonant transmission pathways on the Hilbert space graph, we provide a complementary perspective to real-space and spectral probes, revealing how the destabilization of the MBL phase at finite sizes stems from the emergence of resonant paths that become progressively rarer and shorter-ranged deep in the localized phase.
format Preprint
id arxiv_https___arxiv_org_abs_2510_18545
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Large deviations in the many-body localization transition: The case of the random-field XXZ chain
Miranda, Greivin Alfaro
Alet, Fabien
Biroli, Giulio
Cugliandolo, Leticia F.
Laflorencie, Nicolas
Tarzia, Marco
Disordered Systems and Neural Networks
Statistical Mechanics
Strongly Correlated Electrons
Quantum Physics
The effect of rare system-wide resonances in the many-body localization (MBL) transition has recently attracted significant attention. They are expected to play a prominent role in the stability of the MBL phase, prompting the development of new theoretical frameworks to properly account for their statistical weight. We employ a method based on an analogy with mean-field disordered glassy systems to characterize the statistics of transmission amplitudes between distant many-body configurations in Hilbert space, and apply it to the random-field XXZ spin chain. By introducing a Lagrange multiplier, which formally plays the role of an effective temperature controlling the influence of extreme outliers in the heavy-tailed distribution of propagators, we identify three distinct regimes: (i) an ergodic phase with uniform spreading in Hilbert space, (ii) an intermediate regime where delocalization is driven by rare, disorder-dependent long-range resonances, and (iii) a robust MBL phase where such resonances cannot destabilize localization. We derive a finite-size phase diagram in the disorder--interaction plane both in the spin and in the Anderson basis that quantitatively agrees with recent numerical results based on real-space spin-spin correlation functions. We further demonstrate that even infinitesimal interactions can destroy the Anderson insulator at finite disorder, with the critical disorder remaining finite down to small interaction strengths. By visualizing resonant transmission pathways on the Hilbert space graph, we provide a complementary perspective to real-space and spectral probes, revealing how the destabilization of the MBL phase at finite sizes stems from the emergence of resonant paths that become progressively rarer and shorter-ranged deep in the localized phase.
title Large deviations in the many-body localization transition: The case of the random-field XXZ chain
topic Disordered Systems and Neural Networks
Statistical Mechanics
Strongly Correlated Electrons
Quantum Physics
url https://arxiv.org/abs/2510.18545