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

Understand

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 2-colored case and 4-colored case with balanced number of Majorana fermion $N$.
• By identifying the maximal symmetries, the independent parity conservation sectors, the minimum (irreducible) Hilbert space, and especially the relevant anti-unitary and unitary operators, we show that the color degree of freedoms lead to novel quantum chaotic behaviours.