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Single-Particle Universality of the Many-Body Spectral Form Factor
Michael O Flynn1,2, Lev Vidmar3,4, Tatsuhiko N Ikeda1,5,6
1Boston University, Department of Physics, Boston, Massachusetts 02215, USA.
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.
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.
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