Slow scrambling in a quantum rotor model with random exchange interactions

In recent years, out-of-time-order correlation functions (OTOC) have been used to diagnose the onset of information scrambling in a wide class of problems, ranging from black holes to interacting field theories and lattice models. We study the OTOC for a solvable model of a large number (N) of M-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions [1]. At a finite temperature above the quantum critical point separating a spin-glass and a paramagnetic phase, there is no exponential growth of the OTOC of the rotor fields. We show that in this large N, M limit, the random rotor model is integrable, and can be described by random matrix theory. The apparent lack of quasiparticle excitations in this limit arises as a result of disorder averaging and not strong interactions. We also compute the leading 1/M contribution to the OTOC of the rotor fields and find a slow exponential growth.
[1] Solvable spin glass of quantum rotors, J. Ye, S. Sachdev, and N. Read, Phys. Rev. Lett. 70, 4011