Anderson Orthogonality in the Dynamics After a Local Quantum Quench

TL;DR

This paper investigates how Anderson orthogonality affects the dynamics after a local quantum quench in impurity models, using numerical methods to analyze spectral functions and phase transitions.

Contribution

It formulates generalized rules for Anderson orthogonality effects in quantum quenches and demonstrates them through numerical studies of impurity models, including the interacting resonant level model.

Findings

Power-law behavior in spectral functions due to orthogonality

Charge sensing can induce a quantum phase transition

Explicit calculation of orthogonality exponents confirms theoretical predictions

Abstract

We present a systematic study of the role of Anderson orthogonality for the dynamics after a quantum quench in quantum impurity models, using the numerical renormalization group. As shown by Anderson in 1967, the scattering phase shifts of the single-particle wave functions constituting the Fermi sea have to adjust in response to the sudden change in the local parameters of the Hamiltonian, causing the initial and final ground states to be orthogonal. This so-called Anderson orthogonality catastrophe also influences dynamical properties, such as spectral functions. Their low-frequency behaviour shows nontrivial power laws, with exponents that can be understood using a generalization of simple arguments introduced by Hopfield and others for the X-ray edge singularity problem. The goal of this work is to formulate these generalized rules, as well as to numerically illustrate them for quantum quenches in impurity models involving local interactions. As a simple yet instructive example, we use the interacting resonant level model as testing ground for our generalized Hopfield rule. We then analyse a model exhibiting population switching between two dot levels as a function of gate voltage, probed by a local Coulomb interaction with an additional lead serving as charge sensor. We confirm a recent prediction that charge sensing can induce a quantum phase transition for this system, causing the population switch to become abrupt. We elucidate the role of Anderson orthogonality for this effect by explicitly calculating the relevant orthogonality exponents.