Flux quench in a system of interacting spinless fermions in one dimension

TL;DR

This paper investigates the non-equilibrium dynamics of a one-dimensional interacting spinless fermion system after a flux quench, revealing persistent currents in gapless phases and decay in gapped phases, with nonlinear effects depending on interaction type.

Contribution

It provides a detailed numerical analysis of flux quench dynamics in an interacting fermion model, highlighting differences between gapless and gapped regimes and nonlinear effects.

Findings

Persistent current in gapless phases at long times.

Current decays to zero in gapped phases.

Nonlinear effects are stronger for repulsive interactions.

Abstract

We study a quantum quench in a one-dimensional spinless fermion model (equivalent to the XXZ spin chain), where a magnetic flux is suddenly switched off. This quench is equivalent to imposing a pulse of electric field and therefore generates an initial particle current. This current is not a conserved quantity in presence of a lattice and interactions and we investigate numerically its time-evolution after the quench, using the infinite time-evolving block decimation method. For repulsive interactions or large initial flux, we find oscillations that are governed by excitations deep inside the Fermi sea. At long times we observe that the current remains non-vanishing in the gapless cases, whereas it decays to zero in the gapped cases. Although the linear response theory (valid for a weak flux) predicts the same long-time limit of the current for repulsive and attractive interactions (relation with the zero-temperature Drude weight), larger nonlinearities are observed in the case of repulsive interactions compared with that of the attractive case.