Abstract
The reduced dynamics formalism has recently emerged as a powerful tool to study the dynamics of non-equilibrium quantum impurity models in strongly correlated regimes. Examples include the non-equilibrium Anderson impurity model near the Kondo crossover temperature and the non-equilibrium Holstein model, for which the formalism provides an accurate description of the reduced density matrix of the system for a wide range of timescales. In this work, we generalize the formalism to allow for non-system observables such as the current between the impurity and leads. We show that the equation of motion for the reduced observable of interest can be closed with the equation of motion for the reduced density matrix and demonstrate the new formalism for a generic resonant level model.
Highlights
The study of open quantum impurity models, where the coupling of a small system to multiple baths drives it permanently away from the possibility of an equilibrium state, is an active and rapidly progressing field of research
Several different types of brute-force approaches developed in recent years have been applied to open nonequilibrium quantum systems
If we assume that the initial correlations are either zero to begin with or die out at infinite time, this gives: i LS − κ (z → i0) σ (t → ∞) = 0. (41). This last equation is of particular interest, because it allows us to go from the memory kernel and system Liouvillian directly to the steady state properties of the reduced density matrix, without passing through the dynamics and without any reference to the initial state or correlations of the system
Summary
The study of open quantum impurity models, where the coupling of a small system to multiple baths drives it permanently away from the possibility of an equilibrium state, is an active and rapidly progressing field of research. Several different types of brute-force approaches developed in recent years have been applied to open nonequilibrium quantum systems These include the timedependent numerical renormalization group[17] and functional renormalization group,[18,19,20] time-dependent density matrix renormalization group,[21,22,23,24] iterative[25,26,27,28] and stochastic[29,30,31,32,33] diagrammatic methods, and wavefunction based approaches.[34,35] While the application of these approaches to the the nonequilibrium Holstein, the Anderson impurity, and the spin-fermion models has been very fruitful, they are still restricted to a relatively small range of parameters, typically characterized by a rapid decay to steady-state.
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