Many-Body Level Statistics of Single-Particle Quantum Chaos

Yunxiang Liao, Amit Vikram, and Victor Galitski
Phys. Rev. Lett. 125, 250601 – Published 18 December 2020
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Abstract

We consider a noninteracting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q=2 complex Sachdev-Ye-Kitaev model)—a generic model of single-particle quantum chaos. We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation. Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape. In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction. These results are encoded in an exponential ramp in the spectral form factor, which we show to be a universal feature of nonergodic many-fermion systems embedded in a chaotic medium.

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  • Received 19 June 2020
  • Accepted 26 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.250601

© 2020 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsStatistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Yunxiang Liao1,2, Amit Vikram1,2, and Victor Galitski1,2

  • 1Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
  • 2Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA

See Also

Exponential Ramp in the Quadratic Sachdev-Ye-Kitaev Model

Michael Winer, Shao-Kai Jian, and Brian Swingle
Phys. Rev. Lett. 125, 250602 (2020)

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Vol. 125, Iss. 25 — 18 December 2020

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