2021/04/30 by Yunxiang Liao, Victor Galitski · 20 citations
Physics and Astronomy · #Eigenvalues and eigenvectors #Lyapunov exponent #Mathematical physics #Physics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Random matrix #Spectroscopy and Quantum Chemical Studies #Symmetry breaking #Unitarity #Unitary state #cond-mat.dis-nn #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1103/physrevb.105.l140202
published in Physical review. B./Physical review. B 105(14) (American Physical Society) · 7+26 pages, 2+2 figures
openalex created_date 2021/04/26 · openalex publication_date 2022/04/18 · arxiv created 2022/04/20 · arxiv updated 2022/04/21 · openalex updated_date 2026/08/05
It is suggested that many-body quantum chaos appears as the spontaneous symmetry breaking of unitarity in interacting quantum many-body systems. It has been shown that many-body level statistics, probed by the spectral form factor (SFF) defined as K(\ensuremathη,t)=\ensuremath⟨|Trexp(\ensuremath-\ensuremathηH+itH)|2\ensuremath⟩, is dominated by a diffuson-type mode in a field theory analysis. The key finding of this Letter is that the ``unitary'' \ensuremathη=0 case is different from the \ensuremathη\ensuremath→0^\ifmmode±\else\textpm\fi limit, with the latter leading to a finite mass of these modes due to interactions. This mass suppresses a rapid exponential ramp in the SFF, which is responsible for the fast emergence of Poisson statistics in the noninteracting case, and gives rise to a nontrivial random matrix structure of many-body levels. The interaction-induced mass in the SFF shares similarities with the dephasing rate in the theory of weak localization and the Lyapunov exponent of the out-of-time-ordered correlators.