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 a 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 selfconsistent 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.

Multiple amplitude modes in strongly coupled phonon-mediated superconductors

“…(1) is mapped onto a singlesite impurity model, whose action in the Nambu formalism reads 0,σ (t,t ) is the Weiss Green's function on the KB contour, which is determined selfconsistently so that the impurity Green's functionĜ imp (t,t ) = −i T C (t) † (t ) and the impurity self-energyˆ coincide with the local Green's function for electrons,Ĝ(t,t ) = −i T C i (t) † i (t ) , and the momentum-independent selfenergy in the original lattice problem [32]. Here, T C is the contour ordering operator.…”

“…In principle, even in a nonequilibrium setup, one can solve the problem with a quantum Monte Carlo (QMC) impurity solver [32,33]. However, because of a dynamical sign problem [33] it is difficult to access the time scales needed to study the relatively slow dynamics of phonons and order parameters.…”

“…This quantity can be obtained in the strongly coupled regime by solving the Bethe-Salpeter equation with a frequency-dependent irreducible vertex on the Matsubara axis and by a subsequent numerical analytic continuation for real-frequency information, which would be a bottleneck to this approach. In this paper, instead of directly solving the Bethe-Salpeter equation, we explore the behavior of the collective modes in strongly coupled SCs by simulating the nonequilibrium response to weak perturbations using the nonequilibrium dynamical mean-field theory (DMFT) [32].…”

Towards properties on demand in quantum materials

“…In tandem with improvements in experimental detection capabilities, theoretical predictions of new forms and phases of quantum matter are becoming increasingly precise 6,53,69,104,129,130,151,169,170 . Theory is indispensable for devising driving protocols to realize new quantum phases on demand, beyond the parameter regimes of existing materials.…”

Nonadiabatic exchange-correlation kernel for strongly correlated materials

“…[10] and [11,12], correspondingly). The success of these theories is based on their accuracy -the Bethe ansatz solution is exact in the one-dimensional case and DMFT is very accurate in the limit of high atomic coordination number (and exact in the limit of infinite dimensions/coordination number).…”