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arXiv:2009.04961 · Physical review. B./Physical review. B

Accelerated gap collapse in a Slater antiferromagnet

Antonio Picano, Martin Eckstein

Published Apr 16, 2021• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.103.165118

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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 dynamical phase transitions from antiferromagnetic to paramagnetic states driven by an interaction quench in the fermionic Hubbard model using the nonequilibrium dynamical mean-field theory. We identify two dynamical transition points where the relaxation behavior qualitatively changes: one corresponds to the thermal phase transition at which the order parameter decays critically slowly in a power law ∝t(-1/2), and the other is connected to the existence of nonthermal antiferromagnetic order in systems with effective temperature above the thermal critical temperature. The frequency of the amplitude mode extrapolates to zero as one approaches the nonthermal (quasi)critical point, and thermalization is significantly delayed by the trapping in the nonthermal state. A slow relaxation of the nonthermal order is followed by a faster thermalization process.
We study the time evolution of the antiferromagnetic order parameter after interaction quenches in the Hubbard model. Using the nonequilibrium dynamical mean-field formalism, we show that the system, after a quench from intermediate to strong interaction, is trapped in a nonthermal state which is reminiscent of a photodoped state and protected by the slow decay of doublons. If the effective doping of this state is low enough, it exhibits robust antiferromagnetic order, even if the system is highly excited and the thermal state is thus expected to be paramagnetic. We comment on the implication of our findings for the stability of nonthermal superconducting states.
Nonequilibrium time evolution in isolated many-body quantum systems generally results in thermalization. However, the relaxation process can be very slow, and quasistationary nonthermal plateaux are often observed at intermediate times. The paradigmatic example is a quantum quench in an integrable model with weak integrability breaking; for a long time, the state cannot escape the constraints imposed by the approximate integrability. We unveil a new mechanism of prethermalization, based on the presence of a symmetry of the prequench Hamiltonian, which is spontaneously broken at zero temperature and is explicitly broken by the postquench Hamiltonian. The typical time scale of the phenomenon is proportional to the thermal correlation length of the initial state, which diverges as the temperature is lowered. We show that the prethermal quasistationary state can be approximated by a mixed state that violates cluster decomposition property. We consider two examples: the transverse-field Ising chain, where the full-time evolution is computed analytically, and the (nonintegrable) anisotropic next-nearest-neighbor Ising model, which is investigated numerically.
We numerically study the dynamics after a parameter quench in the one-dimensional transverse-field Ising model with long-range interactions ($\ensuremath{\propto}1/{r}^{\ensuremath{\alpha}}$ with distance rrr), for finite chains and also directly in the thermodynamic limit. In nonequilibrium, i.e., before the system settles into a thermal state, we find a long-lived regime that is characterized by a prethermal value of the magnetization, which in general differs from its thermal value. We find that the ferromagnetic phase is stabilized dynamically: as a function of the quench parameter, the prethermal magnetization shows a transition between a symmetry-broken and a symmetric phase, even for those values of $\ensuremath{\alpha}$ for which no finite-temperature transition occurs in equilibrium. The dynamical critical point is shifted with respect to the equilibrium one, and the shift is found to depend on $\ensuremath{\alpha}$ as well as on the quench parameters.
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 UUU, 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 UCU_{C}UC​, 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.
Although statistical mechanics describes thermal equilibrium states, these states may or may not emerge dynamically for a subsystem of an isolated quantum many-body system. For instance, quantum systems that are near-integrable usually fail to thermalize in an experimentally realistic time scale, and instead relax to quasi-stationary prethermal states that can be described by statistical mechanics, when approximately conserved quantities are included in a generalized Gibbs ensemble (GGE). We experimentally study the relaxation dynamics of a chain of up to 22 spins evolving under a long-range transverse-field Ising Hamiltonian following a sudden quench. For sufficiently long-range interactions, the system relaxes to a new type of prethermal state that retains a strong memory of the initial conditions. However, the prethermal state in this case cannot be described by a standard GGE; it rather arises from an emergent double-well potential felt by the spin excitations. This result shows that prethermalization occurs in a broader context than previously thought, and reveals new challenges for a generic understanding of the thermalization of quantum systems, particularly in the presence of long-range interactions.