Quantum and Classical Dynamics with Random Permutation Circuits

Abstract

Understanding thermalisation in quantum many-body systems is among the most enduring problems in modern physics. A particularly interesting question concerns the role played by quantum mechanics in this process, i.e. whether thermalisation in quantum many-body systems is fundamentally different from that in classical many-body systems and, if so, which of its features are genuinely quantum. Here we study this question in minimally structured many-body systems which are only constrained to have local interactions, i.e. local random circuits. We introduce a class of random permutation circuits (RPCs), where the gates locally permute basis states modelling generic microscopic classical dynamics, and compare them to random unitary circuits (RUCs), a standard toy model for generic quantum dynamics. We show that, like RUCs, RPCs permit the analytical computation of several key quantities such as out-of-time order correlators (OTOCs), or entanglement entropies. RPCs can be interpreted both as quantum or classical dynamics, which we use to find similarities and differences between the two. Performing the average over all random circuits, we discover a series of exact relations, connecting quantities in RUC and (quantum) RPCs. In the classical setting, we obtain similar exact results relating (quantum) purity to (classical) growth of mutual information and (quantum) OTOCs to (classical) decorrelators. Our results indicate that despite of the fundamental differences between quantum and classical systems, their dynamics exhibits qualitatively similar behaviours.

26 (15+11) pages, 2 figures; v2 minor modifications

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Cited by in corpus (8)

• Exactly solvable many-body dynamics from space-time duality
• Theory of Irreversibility in Quantum Many-Body Systems
• Entanglement dynamics and Page curves in random permutation circuits
• Random Permutation Circuits Beyond Qubits are Quantum Chaotic
• Phase transition from localization to chaos in classical many-body system
• Coherence-induced deep thermalization transition in random permutation quantum dynamics
• Bridging Classical and Quantum Information Scrambling with the Operator Entanglement Spectrum
• Crystalline Spectral Form Factors