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Many-body localization (MBL) breaks ergodicity in quantum systems, analogous to Anderson localization. This study uses an ergodicity indicator to identify the MBL transition in disordered spin chains.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Statistical mechanics

Background:

  • Ergodic properties characterize states of matter.
  • Many-body localization (MBL) is a key phenomenon breaking ergodicity in quantum systems.
  • Random matrix theory provides a framework for quantum chaos and ergodicity.

Purpose of the Study:

  • To numerically investigate spectral statistics of disordered interacting spin chains.
  • To characterize the ergodicity breaking transition in systems exhibiting MBL.
  • To explore analogies between MBL and Anderson localization transitions.

Main Methods:

  • Numerical study of spectral statistics in disordered interacting spin chains.
  • Utilizing an ergodicity indicator g, defined by the ratio of Heisenberg time (t_H) and Thouless time (t_Th).
  • Employing a Berezinskii-Kosterlitz-Thouless correlation length for scaling analysis.

Main Results:

  • The ergodicity breaking transition occurs when t_H ≈ t_Th, leading to a system-size independent ergodicity indicator.
  • A scaling solution for the ergodicity indicator g is observed across the transition.
  • Finite-size scaling analysis reveals a flow towards the quantum chaotic regime with increasing system size.

Conclusions:

  • The ergodicity breaking transition in many-body systems shares analogies with the Anderson localization transition.
  • The proposed ergodicity indicator and scaling analysis provide a method for detecting the MBL transition in finite systems.
  • Numerical results support the theoretical framework for understanding ergodicity breaking in quantum many-body systems.