# Out-of-equilibrium density dynamics of a spinful Luttinger liquid

## TL;DR

This paper explores how a one-dimensional spinful fermionic system's particle density evolves after a finite-duration interaction quench, revealing the formation of correlated states influenced by quench protocols and boundary effects.

## Contribution

It introduces a detailed analysis of out-of-equilibrium density dynamics in a spinful Luttinger liquid, including the impact of umklapp perturbations and quench duration on Wigner molecule formation.

## Key findings

- Wigner molecule formation depends on quench duration.
- Propagation of light-cone perturbations drives correlated state creation.
- System behavior varies between sudden and adiabatic regimes.

## Abstract

Using a Luttinger liquid theory we investigate the time evolution of the particle density of a one-dimensional spinful fermionic system with open boundaries and subject to a finite-duration quench of the inter-particle interaction. Taking into account also the turning on of an umklapp perturbation to the system Hamiltonian as a result of the quench, we study the possible formation of a Wigner molecule inside the system, focusing in particular on the sudden and adiabatic regimes. We show that the creation of this correlated state is essentially due to the propagation of "light-cone" perturbations through system which arise after both switching on and switching off the quenching protocol and that its behavior strongly depends on the quench duration.