Quantum to classical crossover in many-body chaos and scrambling from relaxation in a glass

Abstract

Chaotic quantum systems with Lyapunov exponent ${\lambda }_{\mathrm{L}}$ obey an upper bound ${\lambda }_{\mathrm{L}}\le 2\pi k_{\mathrm{B}}T/\hslash$ at temperature $T$, implying a divergence of the bound in the classical limit $\hslash \to 0$. Following this trend, does a quantum system necessarily become `more chaotic' when quantum fluctuations are reduced? Moreover, how do symmetry breaking and associated non-trivial dynamics influence the interplay of quantum mechanics and chaos? We explore these questions by computing ${\lambda }_{\mathrm{L}}(\hslash ,T)$ in the quantum spherical $p$-spin glass model, where $\hslash$ can be continuously varied. We find that quantum fluctuations, in general, make paramagnetic phase less and the replica symmetry-broken 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 $\hslash$ close to the dynamical glass transition temperature $T_d$. Our results in the classical limit ($\hslash \to 0$) naturally describe chaos in super-cooled liquid in structural glasses. We find a maximum in ${\lambda }_{\mathrm{L}}(T)$ substantially above $T_d$, concomitant with the crossover from simple to slow 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.

6 pages, 4 figures

References in corpus (6)

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• Theory of universal incoherent metallic transport
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Scrambling versus relaxation in Fermi and non-Fermi liquids
• Phase diagram of the $p$-spin-interacting spin glass with ferromagnetic bias and a transverse field in the infinite-$p$ limit
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Cited by in corpus (6)

• Quantum-to-classical crossover in the spin glass dynamics of cavity QED simulators
• Classical route to ergodicity and scarring in collective quantum systems
• Probing chaos in the spherical p-spin glass model
• Information scrambling and butterfly velocity in quantum spin glass chains
• Correspondence between excited energy eigenstates and local minima of energy landscape in quantum spin systems
• Sachdev-Ye-Kitaev Model in a Quantum Glassy Landscape