Influence of a bosonic environment onto the non-equilibrium dynamics of local electronic states in a quantum impurity system close to a quantum phase transition

TL;DR

This paper studies how a bosonic environment affects the non-equilibrium behavior of a quantum impurity system near a quantum phase transition, revealing different dynamical regimes and the conditions for thermalization.

Contribution

It demonstrates that the non-equilibrium dynamics can be understood via an effective single-impurity model with a renormalized Coulomb interaction, depending on the bath exponent type.

Findings

Steady states are reached at long times in all regimes.

Thermalization occurs only in the strong coupling regime.

Deviations from thermal equilibrium are linked to proximity to the quantum critical point.

Abstract

We investigate the influence of an additional bosonic bath onto the real-time dynamics of a localized orbital coupled to conduction band with an energy-dependent coupling function $\Gamma(\varepsilon) \propto |\varepsilon|^r$. Recently, a rich phase diagram has been found in this Bose-Fermi Anderson model, where the transitions between competing ground states are governed by quantum critical points. In addition to a transition between a Kondo singlet and a local moment, a localized phase has been established once the coupling to a sub-ohmic bosonic bath exceeds a critical value. Using the time-dependent numerical renormalization group approach, we show that the non-equilibrium dynamics with F-type of bath exponents can be fully understand within an effective single-impurity Anderson model using a renormalized local Coulomb interaction $U_{\rm ren}$. For regimes with B-type of bath exponents, the nature of the bosonic bath and the coupling strength has a profound impact on the electron dynamics which can only partially be understood using an appropriate $U_{\rm ren}$. The local expectation values always reach a steady state at very long times. By a scaling analysis for $\Lambda \to 1^+$, we find thermalization of the system only in the strong coupling regime. In the local moment and in the localized phase significant deviations between the steady-state value and the thermal equilibrium value are found that are related to the distance to the quantum critical point.