Universal quench dynamics of interacting quantum impurity systems

TL;DR

This paper investigates the universal quench dynamics in various interacting quantum impurity systems, exploring how they exhibit scale-invariant behavior similar to non-interacting models using advanced theoretical methods.

Contribution

It demonstrates that universal scaling and large-time behavior predicted by field theory also apply to interacting impurity models analyzed with renormalization group techniques.

Findings

Universal scaling observed in interacting systems

Field theory predictions match microscopic model dynamics

Large-time behavior consistent with non-interacting cases

Abstract

The equilibrium physics of quantum impurities frequently involves a universal crossover from weak to strong reservoir-impurity coupling, characterized by single-parameter scaling and an energy scale $T_K$ (Kondo temperature) that breaks scale invariance. For the non-interacting resonant level model, the non-equilibrium time evolution of the Loschmidt echo after a local quantum quench was recently computed explicitely [R. Vasseur, K. Trinh, S. Haas, and H. Saleur, Phys. Rev. Lett. 110, 240601 (2013)]. It shows single-parameter scaling with variable $T_K t$. Here, we scrutinize whether similar universal dynamics can be observed in various interacting quantum impurity systems. Using density matrix and functional renormalization group approaches, we analyze the time evolution resulting from abruptly coupling two non-interacting Fermi or interacting Luttinger liquid leads via a quantum dot or a direct link. We also consider the case of a single Luttinger liquid lead suddenly coupled to a quantum dot. We investigate whether the field theory predictions for the universal scaling as well as for the large time behavior successfully describe the time evolution of the Loschmidt echo and the entanglement entropy of microscopic models.