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Many-Body Delocalization as a Quantum Avalanche.

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Summary
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We introduce a multiscale diagonalization scheme to analyze disordered one-dimensional chains, focusing on the many-body localization (MBL) transition. Our findings suggest systems are localized at criticality, with delocalization driven by quantum avalanches on the ergodic side.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Statistical Mechanics
  • Disordered Quantum Systems

Background:

  • Understanding the transition between many-body localization (MBL) and the ergodic phase in disordered quantum systems is a key challenge.
  • The role of resonant spots and the validity of the eigenstate thermalization hypothesis (ETH) are central to this transition.

Purpose of the Study:

  • To develop a multiscale diagonalization scheme for studying disordered one-dimensional chains.
  • To investigate the critical behavior and the nature of the MBL-ergodic transition.
  • To clarify the interplay between localization, thermalization, and the influence of ergodic regions.

Main Methods:

  • Development and application of a novel multiscale diagonalization scheme.
  • Focus on the dichotomy between MBL and the ETH.
  • Analytical illustration using a mean-field approximation.

Main Results:

  • Under natural assumptions, the system is localized with probability one at criticality.
  • Delocalization on the ergodic side is driven by a quantum avalanche initiated by large ergodic spots, whose size diverges at the transition.
  • On the MBL side, localization length relates to maximal entropy density, with a divergent length scale associated with ergodic spot inclusions.
  • The mean-field approximation predicts a power-law distribution for thermal inclusions at criticality.

Conclusions:

  • The study provides a detailed theoretical framework for understanding the MBL-ergodic transition in one-dimensional disordered systems.
  • It elucidates the mechanisms of localization and delocalization, highlighting the critical role of resonant and ergodic spots.
  • The findings offer insights into the statistical properties of thermal inclusions at the critical point.