New theoretical approaches for correlated systems in nonequilibrium

Abstract

We review recent developments in the theory of interacting quantum many-particle systems that are not in equilibrium. We focus mainly on the nonequilibrium generalizations of the flow equation approach and of dynamical mean-field theory (DMFT). In the nonequilibrium flow equation approach one first diagonalizes the Hamiltonian iteratively, performs the time evolution in this diagonal basis, and then transforms back to the original basis, thereby avoiding a direct perturbation expansion with errors that grow linearly in time. In nonequilibrium DMFT, on the other hand, the Hubbard model can be mapped onto a time-dependent self-consistent single-site problem. We discuss results from the flow equation approach for nonlinear transport in the Kondo model, and further applications of this method to the relaxation behavior in the ferromagnetic Kondo model and the Hubbard model after an interaction quench. For the interaction quench in the Hubbard model, we have also obtained numerical DMFT results using quantum Monte Carlo simulations. In agreement with the flow equation approach they show that for weak coupling the system relaxes to a "prethermalized" intermediate state instead of rapid thermalization. We discuss the description of nonthermal steady states with generalized Gibbs ensembles.

19 pages, 6 figures, submitted to Eur. Phys. J. for publication in the Special Topics volume "Cooperative Phenomena in Solids: Metal-Insulator Transitions and Ordering of Microscopic Degrees of Freedom"

References in corpus (25)

• Thermalization and its mechanism for generic isolated quantum systems
• The Kernel Polynomial Method
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• The Luttinger model following a sudden interaction switch-on
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Quench dynamics across quantum critical points
• Strongly correlated fermions after a quantum quench
• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• Theoretical description of time-resolved photoemission spectroscopy: application to pump-probe experiments
• Effective thermal dynamics following a quantum quench in a spin chain
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Correlated electron systems periodically driven out of equilibrium: Floquet + DMFT formalism
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Relaxation of a one-dimensional Mott insulator after an interaction quench
• Nonequilibrium Steady State of Photoexcited Correlated Electrons in the Presence of Dissipation
• Quenching Bloch oscillations in a strongly correlated material
• Steady-state nonequilibrium density of states of driven strongly correlated lattice models in infinite dimensions
• Theory of time-resolved optical spectroscopy on correlated electron systems
• Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory
• Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory
• Real-time renormalization group in frequency space: A 2-loop analysis of the nonequilibrium anisotropic Kondo model at finite magnetic field
• Measuring correlated electron dynamics with time-resolved photoemission spectroscopy
• Introduction to the Keldysh formalism and applications to time-dependent density-functional theory
• Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice

Cited by in corpus (13)

• Solving nonequilibrium dynamical mean-field theory using matrix product states
• Non-equilibrium electronic transport in a one-dimensional Mott insulator
• Non-perturbative stochastic method for driven spin-boson model
• Theoretical description of high-order harmonic generation in solids
• Nonequilibrium quantum dynamics of a charge carrier doped into a Mott insulator
• Typicality of Prethermalization
• Multiconfiguration time-dependent Hartree impurity solver for nonequilibrium dynamical mean-field theory
• Imaginary-time quantum many-body theory out of equilibrium I: Formal equivalence to Keldysh real-time theory and calculation of static properties
• Nonequilibrium Dynamical Cluster Approximation study of the Falicov-Kimball Model
• Tailored jump operators for purely dissipative quantum magnetism
• Auxiliary master equation approach within stochastic wave functions: Application to the Interacting Resonant Level Model
• Non-linear response to electric field in extended Hubbard models
• The excitation operator method in the spin dynamics of the one-dimensional XXZ model