Real-time approach and nonequilibrium dynamics

Marco Schirò

We extend the recently developed real-time diagrammatic Monte Carlo method, in its hybridization expansion formulation, to the full Kadanoff-Baym-Keldysh contour. This allows us to study real-time dynamics in correlated impurity models starting from an arbitrary, even interacting, initial density matrix. As a proof of concept, we apply the algorithm to study the nonequilibrium dynamics after a local quantum quench in the Anderson impurity model. Being a completely general approach to real-time dynamics in quantum impurity models, it can be used as a solver for nonequilibrium dynamical mean field theory.

Leonid V. Keldysh

Markus Heyl, Matthias Vojta C

In this work we formulate the nonequilibrium dynamical renormalization group (ndRG). The ndRG represents a general renormalization-group scheme for the analytical description of the real-time dynamics of complex quantum many-body systems. In particular, the ndRG incorporates time as an additional scale which turns out to be important for the description of the long-time dynamics. It can be applied to both translational-invariant and disordered systems. As a concrete application, we study the real-time dynamics after a quench between two quantum critical points of different universality classes. We achieve this by switching on weak disorder in a one-dimensional transverse-field Ising model initially prepared at its clean quantum critical point. By comparing to numerically exact simulations for large systems, we show that the ndRG is capable of analytically capturing the full crossover from weak to infinite randomness. We analytically study signatures of localization in both real space and Fock space.

Leonid V. Keldysh

Emanuel Gull, David R. Reichman, Andrew J. Millis

A Monte Carlo sampling of diagrammatic corrections to the noncrossing approximation is shown to provide numerically exact estimates of the long-time dynamics and steady-state properties of nonequilibrium quantum impurity models. This ``bold'' expansion converges uniformly in time and significantly ameliorates the sign problem that has heretofore limited the power of real-time Monte Carlo approaches to strongly interacting real-time quantum problems. The approach enables the study of previously intractable problems ranging from generic long-time nonequilibrium transport characteristics in systems with large on-site repulsion to the direct description of spectral functions on the real frequency axis in dynamical mean field theory.

Robin B. Stinchcombe, T. Hanney