Matrix-valued Boltzmann equation for the non-integrable Hubbard chain

Abstract

The standard Fermi-Hubbard chain becomes non-integrable by adding to the nearest neighbor hopping additional longer range hopping amplitudes. We assume that the quartic interaction is weak and investigate numerically the dynamics of the chain on the level of the Boltzmann type kinetic equation. Only the spatially homogeneous case is considered. We observe that the huge degeneracy of stationary states in case of nearest neighbor hopping is lost and the convergence to the thermal Fermi-Dirac distribution is restored. The convergence to equilibrium is exponentially fast. However for small n.n.n. hopping amplitudes one has a rapid relaxation towards the manifold of quasi-stationary states and slow relaxation to the final equilibrium state.

9 figures

References in corpus (7)

• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Dynamical phase transition in correlated fermionic lattice systems
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids
• Matrix-valued Boltzmann Equation for the Hubbard Chain
• Collisional invariants for the phonon Boltzmann equation
• Boltzmann-type approach to transport in weakly interacting one-dimensional fermionic systems

Cited by in corpus (21)

• Signatures of rare states and thermalization in a theory with confinement
• Hydrodynamic long-time tails after a quantum quench
• Hydrodynamics of weak integrability breaking
• Thermalization and light cones in a model with weak integrability breaking
• Quench dynamics of one-dimensional bosons in a commensurate periodic potential: A quantum kinetic equation approach
• Prethermalisation and Thermalisation in the Entanglement Dynamics
• Thermalization rates in the one dimensional Hubbard model with next-to-nearest neighbor hopping
• Large-scale universality in quantum reaction-diffusion from Keldysh field theory
• Derivation of a Matrix-valued Boltzmann Equation for the Hubbard Model
• Tunable transport in the mass-imbalanced Fermi-Hubbard model
• Integrability breaking in the Rule 54 cellular automaton
• Universal late-time dynamics in isolated one-dimensional statistical systems with topological excitations
• Relaxation of photoexcitations in polaron-induced magnetic microstructures
• Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory
• Matrix-valued Quantum Lattice Boltzmann Method
• Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation
• Reaction-diffusion dynamics of the weakly dissipative Fermi gas
• Short-lived lattice quasiparticles for strongly interacting fluids
• Quantum Boltzmann equation for spin-dependent reactions in the kinetic regime
• Anomalous Landau damping and algebraic thermalization in two-dimensional superfluids far from equilibrium
• Dynamics of the Bose-Hubbard Chain for Weak Interactions