Abstract
Spectral correlations are a powerful tool to study the dynamics of quantum many-body systems. For Hermitian Hamiltonians, quantum chaotic motion is related to random matrix theory spectral correlations. Based on recent progress in the application of spectral analysis to non-Hermitian quantum systems, we show that local level statistics, which probe the dynamics around the Heisenberg time, of a non-Hermitian -body Sachdev-Ye-Kitev (nHSYK) model with Majorana fermions, and its chiral and complex-fermion extensions, are also well described by random matrix theory for , while for , they are given by the equivalent of Poisson statistics. For that comparison, we combine exact diagonalization numerical techniques with analytical results obtained for some of the random matrix spectral observables. Moreover, depending on and , we identify 19 out of the 38 non-Hermitian universality classes in the nHSYK model, including those corresponding to the tenfold way. In particular, we realize explicitly 14 out of the 15 universality classes corresponding to non-pseudo-Hermitian Hamiltonians that involve universal bulk correlations of classes and , beyond the Ginibre ensembles. These results provide strong evidence of striking universal features in nonunitary many-body quantum chaos, which in all cases can be captured by nHSYK models with .
- Received 22 October 2021
- Accepted 24 March 2022
DOI:https://doi.org/10.1103/PhysRevX.12.021040
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Two distinct features of black holes are that the number of quantum states increases exponentially with their energy and that information that falls into a black hole is maximally scrambled. Interestingly, these are also properties of the Sachdev-Ye-Kitaev (SYK) model, which describes how fermions interact in a complex system. In this paper, we analyze a version of the SYK model that gives up the conservation of probability. This is relevant when the SYK model is coupled to the environment, so that probability flows out of the system and is not conserved. We analyze variants of such models, which scramble information in different ways, and address how we can classify the many types of probability-nonconserving SYK models that exist.
We find that basic probability-nonconserving SYK models follow the same classification as nine of the ten classes of the probability-conserving random matrix ensembles, despite the spectra and scrambling properties being completely different. We also find variants of these SYK models go beyond these ten classes. The simplest model in each class is a matrix with random entries only constrained by the symmetries of the model. We confirm numerically that the scrambling properties of the probability-nonconserving SYK model are given by these random matrices—they are in the same universality class.
Our work paves the way toward an extension of a celebrated conjecture that connects chaos in quantum systems and random matrices to the realm of dynamical systems that do not conserve probability. Future work could examine the extent to which scrambling properties are universal, the necessary conditions to fall into one of the nine universality classes, and the timescale for scrambling to become universal.
