# Universal Entanglement Dynamics following a Local Quench

## TL;DR

This paper investigates the universal behavior of entanglement dynamics after a local quench in quantum wires, revealing a crossover function governed by the Kondo temperature and supported by analytical and numerical methods.

## Contribution

It introduces a universal crossover formula for entanglement growth after a local quench, connecting it to the Kondo temperature and employing integrable models and numerical validation.

## Key findings

- Large-time entanglement follows a logarithmic growth.
- Intermediate time regime described by a universal function F(tT_K).
- Analytic and numerical methods confirm the crossover behavior.

## Abstract

We study the time dependence of the entanglement between two quantum wires after suddenly connecting them via tunneling through an impurity. The result at large times is given by the well known formula $S(t) \approx {1\over 3}\ln {t}$. We show that the intermediate time regime can be described by a universal cross-over formula $S=F(tT_K)$, where $T_K$ is the crossover (Kondo) temperature: the function $F$ describes the dynamical "healing" of the system at large times. We discuss how to obtain analytic information about $F$ in the case of an integrable quantum impurity problem using the massless Form-Factors formalism for twist and boundary condition changing operators. Our results are confirmed by density matrix renormalization group calculations and exact free fermion numerics.