2020/05/31 by Yunxiang Liao, Amit Vikram, Victor Galitski
Physics and Astronomy · #Chaotic #Eigenvalues and eigenvectors #Fermion #Identical particles #Many-body problem #Opinion Dynamics and Social Influence #Physics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Random matrix #Statistical physics #Unitary state #cond-mat.dis-nn #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1103/physrevlett.125.250601
published as Phys. Rev. Lett. 125, 250601 (2020) · Published version. 5+19 pages, 2+2 figures
arxiv created 2020/12/18 · openalex publication_date 2020/12/18 · arxiv updated 2020/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.