# Quench-induced entanglement and relaxation dynamics in Luttinger liquids

## TL;DR

This paper studies how a quantum quench in a Luttinger liquid creates transient entanglement and affects relaxation, revealing universal decay laws and implications for transport and energy fractionalization.

## Contribution

It demonstrates the emergence and decay of quench-induced entanglement in Luttinger liquids and links it to universal relaxation dynamics observable in transport properties.

## Key findings

- Entanglement between right- and left-moving excitations appears transiently after a quench.
- Long-time decay of spectral properties follows a universal $t^{-2}$ law.
- Energy fractionalization reveals the universal decay, offering a new way to study relaxation mechanisms.

## Abstract

We investigate the time evolution towards the asymptotic steady state of a one dimensional interacting system after a quantum quench. We show that at finite time the latter induces entanglement between right- and left- moving density excitations, encoded in their cross-correlators, which vanishes in the long-time limit. This behavior results in a universal time-decay in system spectral properties $ \propto t^{-2} $, in addition to non-universal power-law contributions typical of Luttinger liquids. Importantly, we argue that the presence of quench-induced entanglement clearly emerges in transport properties, such as charge and energy currents injected in the system from a biased probe, and determines their long-time dynamics. In particular, energy fractionalization phenomenon turns out to be a promising platform to observe the universal power-law decay $ \propto t^{-2} $ induced by entanglement and represents a novel way to study the corresponding relaxation mechanism.