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arXiv:2606.05293

Breakdown of Thermalization from Real-Time Dynamics in the Two-Dimensional Hubbard Model

Alessandro Sinibaldi, Luciano Loris Viteritti, Riccardo Rende, Fakher F. Assaad, Giuseppe Carleo

cond-mat.str-elcond-mat.dis-nnquant-phSubmitted Jun 3, 2026• Announced Jun 5, 2026• 0 citations
v1 · Jun 3, 2026v2 · Jul 31, 2026
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Abstract

Thermalization in strongly correlated fermionic systems remains a central open problem in quantum many-body physics. In this work, we investigate the real-time dynamics and the approach to thermalization in the two-dimensional Hubbard model, a paradigmatic framework for correlated electrons, relevant to high-temperature superconductivity and ultracold quantum simulation. Focusing on the half-filled square lattice, we monitor the time evolution of the double occupancy following a quench in the on-site interaction $U$, and assess whether its long-time value is captured by a canonical thermal ensemble. We employ time-dependent variational Monte Carlo methods combined with transformer-based Neural-Network Quantum States to accurately describe the nonequilibrium dynamics of fermions, especially for the behavior at long times, thereby accessing regimes that were previously inaccessible to numerical simulations. Our results reveal two distinct dynamical behaviors: for weak to intermediate interactions, the long-time double occupancy agrees with the thermal prediction, consistent with ergodic relaxation; beyond a critical interaction $U_{C}$, the dynamics deviate markedly from the thermal expectation, revealing clear signatures of thermalization breaking. These results establish numerical simulation as a powerful tool to probe nonequilibrium quantum phenomena in correlated fermionic matter.

Comments
10 pages, 7 figures

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Current quantum simulation experiments are starting to explore nonequilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and timescales. Therefore, the question emerges as to which observables are best suited to study the dynamics in such quantum many-body systems. Using machine learning techniques, we investigate the dynamics and, in particular, the thermalization behavior of an interacting quantum system that undergoes a nonequilibrium phase transition from an ergodic to a many-body localized phase. We employ supervised and unsupervised training methods to distinguish nonequilibrium from equilibrium data, using the network performance as a probe for the thermalization behavior of the system. We test our methods with experimental snapshots of ultracold atoms taken with a quantum gas microscope. Our results provide a path to analyze highly entangled large-scale quantum states for system sizes where numerical calculations of conventional observables become challenging.
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