Solving quantum impurity problems in and out of equilibrium with variational approach

TL;DR

This paper introduces a versatile variational method for solving quantum impurity problems both in and out of equilibrium, effectively capturing complex correlations and dynamics in spin-impurity systems.

Contribution

A new canonical transformation combined with Gaussian states enables efficient modeling of impurity-bath correlations in quantum impurity problems.

Findings

Successfully applied to anisotropic and two-lead Kondo models

Studied non-equilibrium phenomena like long-time crossover in ferromagnetic Kondo model

Achieved accurate spatiotemporal dynamics and universal behavior predictions

Abstract

A versatile and efficient variational approach is developed to solve in- and out-of-equilibrium problems of generic quantum spin-impurity systems. Employing the discrete symmetry hidden in spin-impurity models, we present a new canonical transformation that completely decouples the impurity and bath degrees of freedom. Combining it with Gaussian states, we present a family of many-body states to efficiently encode nontrivial impurity-bath correlations. We demonstrate its successful application to the anisotropic and two-lead Kondo models by studying their spatiotemporal dynamics and universal behavior in the correlations, relaxation times and the differential conductance. We compare them to previous analytical and numerical results. In particular, we apply our method to study new types of nonequilibrium phenomena that have not been studied by other methods, such as long-time crossover in the ferromagnetic easy-plane Kondo model. The present approach will be applicable to a variety of unsolved problems in solid-state and ultracold-atomic systems.