Quantum to classical crossover in many-body chaos in a glass

Surajit Bera, K. Y. Venkata Lokesh, Sumilan Banerjee

Published 2021-05-27Version 1

Chaotic quantum systems with Lyapunov exponent $\lambda_\mathrm{L}$ obey an upper bound $\lambda_\mathrm{L}\leq 2\pi k_\mathrm{B}T/\hbar$ at temperature $T$, implying a divergence of the bound in the classical limit $\hbar\to 0$. Following this trend, does a quantum system necessarily become `more chaotic' when quantum fluctuations are reduced? We explore this question by computing $\lambda_\mathrm{L}(\hbar,T)$ in the quantum spherical $p$-spin glass model, where $\hbar$ can be continuously varied. We find that quantum fluctuations, in general, make paramagnetic phase less chaotic and the spin glass phase more chaotic. We show that the approach to the classical limit could be non-trivial, with non-monotonic dependence of $\lambda_\mathrm{L}$ on $\hbar$ close to the dynamical glass transition temperature $T_d$. Our results in the classical limit ($\hbar\to 0$) naturally describe chaos in super-cooled liquid in structural glasses. We find a crossover from strong to weak chaos substantially above $T_d$, concomitant with the onset of two-step glassy relaxation. We further show that $\lambda_\mathrm{L}\sim T^\alpha$, with the exponent $\alpha$ varying between 2 and 1 from quantum to classical limit, at low temperatures in the spin glass phase. Our results reveal intricate interplay between quantum fluctuations, glassy dynamics and chaos.