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 dynamical behaviors: for weak to intermediate interactions, the double occupancy rapidly approaches the thermal prediction, consistent with ergodic evolution; beyond a critical interaction $U_{C}$ , the dynamics remains distinct from the thermal expectation on the timescales investigated, revealing signatures of a prethermal plateau delaying fast relaxation. These results establish numerical simulation as a powerful tool to probe nonequilibrium quantum phenomena in correlated fermionic matter.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 dynamical behaviors: for weak to intermediate interactions, the double occupancy rapidly approaches the thermal prediction, consistent with ergodic evolution; beyond a critical interaction $U_{C}$, the dynamics remains distinct from the thermal expectation on the timescales investigated, revealing signatures of a prethermal plateau delaying fast relaxation. These results establish numerical simulation as a powerful tool to probe nonequilibrium quantum phenomena in correlated fermionic matter.

cond-mat.str-elCross-listedarXiv:2606.05293Jun 5, 20260 citations

Relaxation dynamics in the Fermi-Hubbard model

Wenchao Xu, William McGehee, William Morong +1 more

Bulletin of the American Physical SocietyJun 11, 20150 citations

Probing Transport and Slow Relaxation in the Mass-Imbalanced Fermi-Hubbard Model

Nelson Darkwah Oppong, G. Pasqualetti, Oscar Bettermann +4 more

Constraints in the dynamics of quantum many-body systems can dramatically alter transport properties and relaxation timescales even in the absence of static disorder.Here, we report on the observation of such constrained dynamics arising from the distinct mobility of two species in the one-dimensional massimbalanced Fermi-Hubbard model, realized with ultracold ytterbium atoms in a state-dependent optical lattice.By displacing the trap potential and monitoring the subsequent dynamical response of the system, we identify suppressed transport and slow relaxation with a strong dependence on the mass imbalance and interspecies interaction strength, consistent with eventual thermalization for long times.Our observations demonstrate the potential for quantum simulators to provide insights into unconventional relaxation dynamics arising from constraints.Constraints in the dynamics of quantum many-body systems can dramatically alter transport properties and relaxation timescales even in the absence of static disorder.Here, we report on the observation of such constrained dynamics arising from the distinct mobility of two species in the one-dimensional massimbalanced Fermi-Hubbard model, realized with ultracold ytterbium atoms in a state-dependent optical lattice.By displacing the trap potential and monitoring the subsequent dynamical response of the system, we identify suppressed transport and slow relaxation with a strong dependence on the mass imbalance and interspecies interaction strength, consistent with eventual thermalization for long times.Our observations demonstrate the potential for quantum simulators to provide insights into unconventional relaxation dynamics arising from constraints.

arXiv:2011.12411Physical Review XAug 16, 202232 citations

Accelerated gap collapse in a Slater antiferromagnet

Antonio Picano, Martin Eckstein

We study the melting of long-range antiferromagnetic order in the Hubbard model after an interaction quench, using nonequilibrium dynamical mean-field theory. From previous studies, the system is known to quickly relax into a prethermal symmetry-broken state. Using a convergent truncation of the memory integrals in the Kadanoff Baym equations, we unravel the subsequent relaxation dynamics of this state over several orders of magnitude in time. At long times, the prethermal state can be characterized by a single slow variable, which is related to the conduction band population. The dynamics of this variable is highly nonlinear, with a pronounced speedup once the gap falls below a certain value. This behavior indicates that nonthermal order can be self-sustained on some timescale because of a thermalization bottleneck is provided by the gap opened by the long-range order itself. These results cannot be reproduced using simple Fermi's golden rule estimate for the evolution of the conduction band population, and are distinct from the conventional scenario for the relaxation of prethermal states, in which a slow thermalization follows a rapid prethermalization.We study the melting of long-range antiferromagnetic order in the Hubbard model after an interaction quench, using nonequilibrium dynamical mean-field theory. From previous studies, the system is known to quickly relax into a prethermal symmetry-broken state. Using a convergent truncation of the memory integrals in the Kadanoff Baym equations, we unravel the subsequent relaxation dynamics of this state over several orders of magnitude in time. At long times, the prethermal state can be characterized by a single slow variable, which is related to the conduction band population. The dynamics of this variable is highly nonlinear, with a pronounced speedup once the gap falls below a certain value. This behavior indicates that nonthermal order can be self-sustained on some timescale because of a thermalization bottleneck is provided by the gap opened by the long-range order itself. These results cannot be reproduced using simple Fermi's golden rule estimate for the evolution of the conduction band population, and are distinct from the conventional scenario for the relaxation of prethermal states, in which a slow thermalization follows a rapid prethermalization.

arXiv:2009.04961Physical review. B./Physical review. BApr 16, 202114 citations

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 dynamical behaviors: for weak to intermediate interactions, the double occupancy rapidly approaches the thermal prediction, consistent with ergodic evolution; beyond a critical interaction

U_{C}

, the dynamics remains distinct from the thermal expectation on the timescales investigated, revealing signatures of a prethermal plateau delaying fast relaxation. These results establish numerical simulation as a powerful tool to probe nonequilibrium quantum phenomena in correlated fermionic matter.