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Spectral Statistics and Many-Body Quantum Chaos with Conserved Charge.

Aaron J Friedman1,2, Amos Chan1, Andrea De Luca1,3

  • 1Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, University of Oxford, Oxford, OX1 3PU, United Kingdom.

Physical Review Letters
|December 7, 2019
PubMed
Summary
This summary is machine-generated.

We studied spectral statistics in chaotic quantum systems. Our findings reveal diffusion-governed scaling behavior in the spectral form factor, marking the limits of random matrix theory predictions.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter physics

Background:

  • Investigating spectral statistics in quantum systems is crucial for understanding their chaotic behavior.
  • Conserved charges and symmetries play a key role in dictating system dynamics.

Purpose of the Study:

  • To compute the spectral form factor K(t) for a minimal Floquet circuit model with U(1) symmetry.
  • To determine the Thouless time (t_Th) and analyze scaling behavior at and below this time.

Main Methods:

  • Analytical computation of the spectral form factor K(t) using a minimal Floquet circuit model.
  • Relating K(t) to a spin partition function via Trotterization of the spin-1/2 Heisenberg ferromagnet.
  • Employing Bethe ansatz techniques to extract the Thouless time and scaling behavior.

Main Results:

  • The spectral form factor K(t) was analytically computed for the specified model.
  • The Thouless time (t_Th) was extracted, defining the boundary of random matrix behavior.
  • Diffusion-governed scaling behavior for K(t) was identified for times t ≲ t_Th.
  • Numerical results for a generic Floquet spin model confirmed the analytic predictions.

Conclusions:

  • The study provides analytical and numerical insights into spectral statistics of chaotic many-body quantum systems.
  • The findings highlight the transition from random matrix behavior to diffusion-dominated scaling.
  • The results offer a framework for understanding spectral properties in systems with conserved charges and symmetries.