Abstract: I will present some analytical results on quantum chaos by making connections with the eigenstate thermalization hypothesis. All these results are supported by numerical simulations.
First, we derive a closed formula for calculating out-of-time-ordered correlators (OTOC) at late times in chaotic spin chains. For generic local operators, the formula shows a power-law scaling of late-time OTOC with system size. We connect this result with the idea of approximating chaotic dynamics by a random unitary.
Second, we consider the average entanglement entropy of all eigenstates in chaotic spin chains. We argue for the universality of the subleading correction to the “volume law,” and propose an exact formula for its dependence on the subsystem size. We prove that the entanglement of a generic eigenstate is distinguishable from that of a random state.
Third, we argue that in the SYK model, the entanglement entropy of an eigenstate has the same scaling as the entropy of a microcanonical ensemble, whose energy is a function of the energy of the eigenstate and the subsystem size. Thus, we obtain a volume law with a coefficient depending on the subsystem size.
Joint works with Fernando G.S.L. Brandao, Yong-Liang Zhang, and Yingfei Gu; Nucl. Phys. B 938, 594 and arXiv:1705.07597, 1709.09160
Contact: Lei Wang