Dynamics of disordered interacting quantum systems

Elisheva Elbaz

Eric Dohner, Hanna Terletska, Ka-Ming Tam +2 more

We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean-field theory and the equilibrium coherent potential approximation methods to the nonequilibrium many-body formalism, using the Kadanoff-Baym-Keldysh complex time contour, for the dynamics of interacting disordered systems away from equilibrium. We use our time domain solution to obtain the equilibrium density of states of the disordered interacting system described by the Anderson-Hubbard model, bypassing the necessity for the cumbersome analytical continuation process. We further apply the nonequilibrium solution to the interaction quench problem for an isolated disordered system. Here, the interaction is abruptly changed from zero (noninteracting system) to another constant (finite) value at which it is subsequently kept. We observe via the time dependence of the potential, kinetic, and total energies the effect of disorder on the relaxation of the system as a function of final interaction strength. The real-time approach has the potential to shed light on the fundamental role of disorder in the nonequilibrium dynamics of interacting quantum systems.

Philippe Jacquod

Chakradhar Rangi, Herbert F. Fotso, Hanna Terletska +2 more

We introduce an extension of the nonequilibrium dynamical mean-field theory to incorporate the effects of static random disorder in the dynamics of a many-particle system by integrating out different disorder configurations resulting in an effective time-dependent density-density interaction. We use this method to study the nonequilibrium transient dynamics of a system described by the Fermi Anderson-Hubbard model following an interaction and disorder quench. The method recovers the solution of the disorder-free case for which the system exhibits qualitatively distinct dynamical behaviors in the weak-coupling (prethermalization) and strong-coupling regimes (collapse-and-revival oscillations). However, we find that weak random disorder promotes thermalization. In the weak-coupling regime, the jump in the quasiparticle weight in the prethermal regime is suppressed by random disorder, while in the strong-coupling regime, random disorder reduces the amplitude of the quasiparticle weight oscillations. These results highlight the importance of disorder in the dynamics of realistic many-particle systems.

V. M. Akulin

Jiawei Yan, Philipp Werner

We discuss a nonequilibrium dynamical mean-field framework for simulating inhomogeneous Hubbard models with local disorders. Our approach treats electron interactions and disorders on equal footing, by considering only local dynamical fluctuations. The theory reduces to nonequilibrium dynamical mean-field theory in the presence of only electron-electron interactions and to the coherent potential approximation in noninteracting systems with disorders. Both time-dependent and steady-state problems are treated by implementing the theory on the three-branch Kadanoff-Baym contour and two-branch Schwinger-Keldysh contour, respectively. Benchmarks on a eight-site cube show that the method yields rather accurate spectral functions in both the weakly and strongly interacting regimes. In a cubic lattice, we demonstrate energy conservation after an interaction quench and thermalization after just a few hopping times in both clean and disordered systems. As an application, we study transport through a serial double quantum-dot sandwiched between two leads, focusing on the current and dot occupations after a voltage quench.