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This summary is machine-generated.

We studied fermion systems and found that chaotic single-particle dynamics lead to exponential growth in spectral form factors (SFFs). Introducing interactions causes a crossover to linear growth, consistent with many-body universality.

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Area of Science:

  • Quantum chaos
  • Many-body physics
  • Random matrix theory

Background:

  • Understanding quantum chaos in many-body systems is crucial.
  • Fermionic systems with correlated potentials offer a unique platform to study this.
  • Spectral statistics provide insights into system dynamics.

Purpose of the Study:

  • To investigate the spectral statistics of noninteracting fermions with correlated potentials.
  • To analyze the impact of single-particle chaos on many-body spectral form factors (SFFs).
  • To explore the crossover behavior upon introducing interactions.

Main Methods:

  • Utilizing noninteracting unitary circuits with correlated on-site potentials.
  • Drawing potentials from the circular random matrix ensemble.
  • Exact computation of many-body spectral form factors (SFFs).

Main Results:

  • Single-particle sector exhibits chaotic dynamics.
  • Exact SFFs reveal signatures of single-particle chaos in many-body statistics.
  • Absence of interactions leads to exponential SFF growth.
  • Interactions induce a crossover to linear SFF growth, aligning with many-body random matrix universality.

Conclusions:

  • Exact SFF calculations provide a baseline for studying the transition between single-particle and many-body chaos.
  • Demonstrated exponential SFF growth in noninteracting systems via arguments, scaling collapses, and closed-form evaluation.
  • Established the crossover to linear growth under interactions, confirming many-body random matrix universality.