Universal equilibration dynamics of the Sachdev-Ye-Kitaev model

Year: 2023

Authors: Bandyopadhyay S., Uhrich P., Paviglianiti A., Hauke P.

Autors Affiliation: Univ Trento, Pitaevskii BEC Ctr, CNR INO & Dipartimento Fis, Via Sommar 14, I-38123 Trento, Italy; Int Sch Adv Studies SISSA, via Bonomea 265, I-34136 Trieste, Italy.

Abstract: Equilibrium quantum many-body systems in the vicinity of phase transitions generically manifest universality. In contrast, limited knowledge has been gained on possible univer-sal characteristics in the non-equilibrium evo-lution of systems in quantum critical phases. In this context, universality is generically at-tributed to the insensitivity of observables to the microscopic system parameters and initial conditions. Here, we present such a univer-sal feature in the equilibration dynamics of the Sachdev-Ye-Kitaev (SYK) Hamiltonian- a paradigmatic system of disordered, all-to-all interacting fermions that has been designed as a phenomenological description of quan-tum critical regions. We drive the system far away from equilibrium by performing a global quench, and track how its ensemble average relaxes to a steady state. Employing state-of-the-art numerical simulations for the exact evolution, we reveal that the disorder-averaged evolution of few-body observables, including the quantum Fisher information and low-order moments of local operators, exhibit within numerical resolution a universal equilibration process. Under a straightforward rescaling, data that correspond to different initial states collapse onto a universal curve, which can be well approximated by a Gaussian throughout large parts of the evolution. To reveal the physics behind this process, we formulate a general theoretical framework based on the Novikov-Furutsu theorem. This framework extracts the disorder-averaged dynamics of a many-body system as an effective dissipative evolution, and can have applications beyond this work. The exact non-Markovian evolution of the SYK ensemble is very well captured by Bourret-Markov approximations, which con-trary to common lore become justified thanks to the extreme chaoticity of the system, and universality is revealed in a spectral analysis of the corresponding Liouvillian.

Journal/Review: QUANTUM

Volume: 7      Pages from: 1022-1  to: 1022-24

More Information: We gratefully acknowledge useful discussions with Jean-Philippe Brantut, Julian Sonner, and Ricardo Costa de Almeida. We acknowledge CINECA HPC project ISCRA Class C: ISSYK-HP10CE3PVN and ISSYK-2 (HP10CP8XXF) . We acknowledge support by Provincia Autonoma di Trento and the Google Research Scholar Award ProGauge. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 804305) . This project has benefited from Q@TN, the joint lab between University of Trento, FBK-Fondazione Bruno Kessler, INFN-National Institute for Nuclear Physi cs and CNR-National Research Council.
KeyWords: Many-body Localization; Quantum Simulations; Statistical-mechanics; Thermalization; Entanglement; Propagation; Chaos; Relaxation
DOI: 10.22331/Q-2023-05-24-1022

Citations: 1
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