Nonequilibrium dynamical mean-field theory and its applications

Abstract

The study of nonequilibrium phenomena in correlated lattice systems has developed into one of the most active and exciting branches of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultrafast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultracold atoms in optical lattices provide a new way to control and measure the time evolution of interacting lattice systems with a vastly different characteristic time scale compared to electron systems. A theoretical description of these phenomena is challenging because, first, the quantum-mechanical time evolution of many-body systems out of equilibrium must be computed and second, strong-correlation effects which can be of nonperturbative nature must be addressed. This review discusses the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a self-consistent impurity problem, which becomes exact in infinite dimensions. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. Insights gained into the properties of the infinite-dimensional Hubbard model under strong nonequilibrium conditions are summarized. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photodoping, and collapse-and-revival oscillations in quenched systems. Furthermore, remarkable novel phenomena have been predicted by the nonequilibrium DMFT simulations of correlated lattice systems, including dynamical phase transitions and field-induced repulsion-to-attraction conversions.

Nonequilibrium dynamical mean-field theory based on weak-coupling perturbation expansions: Application to dynamical symmetry breaking in the Hubbard model

“…27,28 Since the dynamical phase transition that we are interested in occurs very far from equilibrium, where the temporal variation of the order parameter is not particularly slow, we need a theoretical description of nonequilibrium many-body systems based on a "microscopic theory," without employing a macroscopic coarsening or a phenomenological description (e.g., the time-dependent Ginzburg-Landau equation). The nonequilibrium dynamical mean-field theory (DMFT) [29][30][31] is one such approach, which has been recently developed. It is a nonequilibrium generalization of the equilibrium DMFT 32 that maps a lattice model onto an effective local impurity problem embedded in a dynamical mean-field bath.…”

SU(3)Semiclassical Representation of Quantum Dynamics of Interacting Spins

“…Perhaps the most powerful methods in equilibrium based on quantum Monte-Carlo are not readily adopted to non-equilibrium systems. The other available methods include: simulations based on exact diagonalization; dynamical renormalization group and related matrix product states methods [1]; dynamical mean field theory based methods [2,3] mostly developed for fermions and only recently applied to bosons [4]; quantum kinetic equations and Keldysh diagrammatic technique [5]; and phase space methods. The latter has recently become a major tool for studying dynamics of various systems, from interacting atomic clocks to the early Universe [6][7][8][9][10][11][12].…”

Mechanism for Negative Differential Conductivity in Holographic Conductors

“…Electric devices which exhibit NDC play an important role in construction of switching circuits and oscillator circuits. NDC has been observed in a wide range of strongly-correlated electron systems [1]. However, we still lack a complete understanding of the mechanism for NDC on the basis of the microscopic theory.…”

“…However, we still lack a complete understanding of the mechanism for NDC on the basis of the microscopic theory. 1 A crucial reson for the difficulty is that we need to deal with physics far from equilibrium.…”