Chaos in a quantum rotor model

Abstract

We study scrambling in a model consisting of a number $N$ of $M$-component quantum rotors coupled by random infinite-range interactions. This model is known to have both a paramagnetic phase and a spin glass phase separated by second order phase transition. We calculate in perturbation theory the squared commutator of rotor fields at different sites in the paramagnetic phase, to leading non-trivial order at large $N$ and large $M$. This quantity diagnoses the onset of quantum chaos in this system, and we show that the squared commutator grows exponentially with time, with a Lyapunov exponent proportional to $\frac{1}{M}$. At high temperature, the Lyapunov exponent limits to a value set by the microscopic couplings, while at low temperature, the exponent exhibits a $T^4$ dependence on temperature $T$.

25 pages, 10 figures

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• Information scrambling at finite temperature in local quantum systems
• Quantum to classical crossover in many-body chaos and scrambling from relaxation in a glass
• Slow scrambling and hidden integrability in a random rotor model
• The quantum $p$-spin glass model: A user manual for holographers