Ultrafast dynamics of finite Hubbard clusters - a stochastic mean-field approach

Abstract

Finite lattice models are a prototype for strongly correlated quantum systems and capture essential properties of condensed matter systems. With the dramatic progress in ultracold atoms in optical lattices, finite fermionic Hubbard systems have become directly accessible in experiments, including their ultrafast dynamics far from equilibrium. Here, we present a theoretical approach that is able to treat these dynamics in any dimension and fully includes inhomogeneity effects. The method consists in stochastic sampling of mean-field trajectories and is found to be more accurate and efficient than current nonequilibrium Green functions approaches. This is demonstrated for Hubbard clusters with up to 512 particles in one, two and three dimensions.

References in corpus (22)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Cold bosonic atoms in optical lattices
• Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
• Finite-size scaling of eigenstate thermalization
• Observation of Elastic Doublon Decay in the Fermi-Hubbard Model
• A Stochastic Mean-Field Approach For Nuclear Dynamics
• Successes and Failures of Kadanoff-Baym Dynamics in Hubbard Nanoclusters
• Quantum Quenches in the Thermodynamic Limit
• Observing the Drop of Resistance in the Flow of a Superfluid Fermi Gas
• Stochastic quantum dynamics beyond mean-field
• Hubbard nanoclusters far from equilibrium
• Expansion dynamics in the one-dimensional Fermi-Hubbard model
• Challenges in Truncating the Hierarchy of Time-Dependent Reduced Density Matrices Equations: Open Problems
• Correlation dynamics during a slow interaction quench in a one-dimensional Bose gas
• The time-dependent exchange-correlation functional for a Hubbard dimer: quantifying non-adiabatic effect
• Expansion velocity of a one-dimensional, two-component Fermi gas during the sudden expansion in the ballistic regime
• Symmetry breaking and fluctuations within stochastic mean-field dynamics: importance of initial quantum fluctuations
• Quantal corrections to mean-field dynamics including pairing
• Few-particle quantum dynamics---comparing Nonequilibrium Green's functions with the generalized Kadanoff-Baym ansatz to density operator theory
• Dynamics of Hubbard nano-clusters following strong excitation
• Creation and dynamics of remote spin-entangled pairs in the expansion of strongly correlated fermions in an optical lattice

Cited by in corpus (29)

• Microscopic phase-space exploration modeling of ${}^{258}$Fm spontaneous fission
• Hubbard nanoclusters far from equilibrium
• Nonequilibrium dynamics in the one-dimensional Fermi-Hubbard model: A comparison of the nonequilibrium Green functions approach and the density matrix renormalization group method
• The G1--G2 Scheme: Dramatic Acceleration of Nonequilibrium Green Functions Simulations Within the Hartree--Fock-GKBA
• Towards an integrated modeling of the plasma-solid interface
• Ultrafast Dynamics of Strongly Correlated Fermions -- Nonequilibrium Green Functions and Selfenergy Approximations
• Quantal diffusion approach for multinucleon transfer processes in the ${}^{58,64}$Ni+${}^{208}$Pb reactions: Toward the production of unknown neutron-rich nuclei
• Role of non-gaussian quantum fluctuations in neutrino entanglement
• Impact of the initial fluctuations on the dissipative dynamics of interacting Fermi systems: A model case study
• Importance of realistic phase space representations of initial quantum fluctuations using the stochastic mean-field approach for fermions
• A simplified BBGKY hierarchy for correlated fermionic systems from a Stochastic Mean-Field approach
• Time Reversal Invariance of quantum kinetic equations II: Density operator formalism
• Dynamical quantum phase transitions in the one-dimensional extended Fermi-Hubbard model
• Nuclear Quantum Many-Body Dynamics: From Collective Vibrations to Heavy-Ion Collisions (2nd edition)
• Accelerating Nonequilibrium Green functions simulations: the G1-G2 scheme and beyond
• Electron correlation effects in superconducting nanowires in and out of equilibrium
• Extending \textit{ab initio} plasma-surface simulations to experimentally relevant scales
• Quantum fluctuations approach to the nonequilibrium $GW$ approximation
• Environment-induced decay dynamics of anti-ferromagnetic order in Mott-Hubbard systems
• Combining phase-space and time-dependent reduced density matrix approach to describe the dynamics of interacting fermions
• Quench dynamics in higher-dimensional Holstein models: Insights from Truncated Wigner Approaches
• Classical and Quantum Theory of Fluctuations for Many-Particle Systems out of Equilibrium
• Toward a Nonequilibrium Green functions approach to diffusion in strongly coupled finite quantum systems
• Photoinduced prethermal order parameter dynamics in the two-dimensional large-$N$ Hubbard-Heisenberg model
• Quantum Fluctuations Approach to the Nonequilibrium $GW$-Approximation II: Density Correlations and Dynamic Structure Factor
• Two-Time Quantum Fluctuations Approach and its Relation to the Bethe--Salpeter Equation
• Systematic large flavor fTWA approach to interaction quenches in the Hubbard model
• Emulation of large-scale qubit registers with a phase-space approach
• Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice