Showing papers by "Jinwu Ye published in 2020"

Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models

Abstract: The random matrix theory (RMT) can be used to classify both topological phases of matter and quantum chaos. We develop a systematic and transformative RMT to classify the quantum chaos in the colored Sachdev-Ye-Kitaev (SYK) model first introduced by Gross and Rosenhaus. Here we focus on the two-colored case and the four-colored case with a balanced number of Majorana fermions $N$. By identifying the maximal symmetries, the independent parity conservation sectors, the minimum (irreducible) Hilbert space, and especially the relevant antiunitary and unitary operators, we show that the color degrees of freedom lead to novel quantum chaotic behaviors. When $N$ is odd, different symmetry operators need to be constructed to make the classifications complete. The two-colored case only shows the threefold Wigner-Dyson way, and the four-colored case shows the tenfold generalized Wigner-Dyson way which may also have nontrivial edge exponents. We also study two- and four-colored hybrid SYK models, which display many salient quantum chaotic features hidden in the corresponding pure SYK models. These features motivate us to develop a systematic RMT to study the energy level statistics of two or four uncorrelated random matrix ensembles. The exact diagonalizations are performed to study both the bulk energy level statistics and the edge exponents and to find excellent agreement with our exact maximal symmetry classifications. Our complete and systematic methods can be easily extended to study the generic imbalanced cases. They may be transferred to the classifications of colored tensor models, quantum chromodynamics with pairings across different colors, quantum black holes, and interacting symmetry protected (or enriched) topological phases.