Crossover physics in the non-equilibrium dynamics of quenched quantum impurity systems

TL;DR

This paper introduces a framework for analyzing non-equilibrium dynamics in integrable quantum impurity systems, revealing crossover behavior linked to the impurity's energy scale, and provides exact calculations for key quantities like the Loschmidt echo.

Contribution

It develops an analytical approach combining boundary problem mapping and form factors to study local quantum quenches in impurity systems, including exact results for the Loschmidt echo and work distribution.

Findings

Identifies crossover physics at the impurity's energy scale T_b.

Provides exact analytical expressions for Loschmidt echo and work distribution.

Validates results with numerical methods in non-interacting cases.

Abstract

A general framework is proposed to tackle analytically local quantum quenches in integrable impurity systems, combining a mapping onto a boundary problem with the form factor approach to boundary-condition-changing operators introduced in Phys. Rev. Lett. 80, 4370 (1998). We discuss how to compute exactly two central quantities of interest: the Loschmidt echo and the distribution of the work done during the quantum quench. Our results display an interesting crossover physics characterized by the energy scale T_b of the impurity corresponding to the Kondo temperature. We discuss in detail the non-interacting case as a paradigm and benchmark for more complicated integrable impurity models, and check our results using numerical methods.