Nonequilibrium Dynamical Mean Field Theory: an auxiliary Quantum Master Equation approach

Abstract

We introduce a versatile method to compute electronic steady state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is mapped onto an auxiliary non-equilibrium impurity problem imbedded in a Markovian environment. The steady state Green's function of the auxiliary system is solved by full diagonalization of the corresponding Lindblad equation. The approach can be regarded as the nontrivial extension of the exact-diagonalization based DMFT to the non-equilibrium case. As a first application, we consider an interacting Hubbard layer attached to two metallic leads and present results for the steady-state current and the non-equilibrium density of states.

Accepted for publication in Phys. Rev. Lett. Final version including supplemental material

References in corpus (22)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Thermalization and its mechanism for generic isolated quantum systems
• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Evidence for a Structurally-driven Insulator-to-metal Transition in VO2: a View from the Ultrafast Timescale
• The Luttinger model following a sudden interaction switch-on
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Dynamical phase transition in correlated fermionic lattice systems
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Atomic three-body loss as a dynamical three-body interaction
• On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems
• Correlated electron systems periodically driven out of equilibrium: Floquet + DMFT formalism
• Nonequilibrium quantum criticality in open electronic systems
• A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Real-time RG in frequency space (RTRG-FS)
• Nonequilibrium Steady State of Photoexcited Correlated Electrons in the Presence of Dissipation
• Super-fermion representation of the Lindblad master equation for the electron transport problem
• Quenching Bloch oscillations in a strongly correlated material
• Superoperator nonequilibrium Green's function theory of many-body systems; Applications to charge transfer and transport in open junctions
• Imaginary-time formulation of steady-state nonequilibrium: application to strongly correlated transport
• Steady-state nonequilibrium density of states of driven strongly correlated lattice models in infinite dimensions
• Nonequilibrium transport and optical properties of model metal--Mott-insulator--metal heterostructures
• Non-equilibrium cluster-perturbation theory

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