Nonlinear effects on charge fractionalization in critical chains

TL;DR

This paper explores how nonlinear effects influence charge fractionalization in a one-dimensional strongly correlated fermionic chain, revealing multiple fractional charges and providing a method to measure nonlinear interaction parameters.

Contribution

It demonstrates that nonlinear dispersion effects lead to multiple fractional charges and offers a protocol for directly measuring nonlinear interaction parameters in quantum systems.

Findings

Observation of at least three fractional charges moving at different velocities

Confirmation that nonlinear Luttinger liquid theory predicts correct low-energy dynamics

Identification of signatures of two-particle bound states at high energies

Abstract

We investigate the generic transport in a one-dimensional strongly correlated fermionic chain beyond linear response. Starting from a Gaussian wave packet with positive momentum on top of the ground state, we find that the numerical time evolution splits the signal into at least three distinct fractional charges moving with different velocities. A fractional left-moving charge is expected from conventional Luttinger liquid theory, but for the prediction of the two separate right-moving packets the nonlinearity of the dispersion must also be taken into account. This out-of-equilibrium protocol therefore allows a direct measurement of nonlinear interaction parameters, which also govern threshold singularities of dynamic response functions. The nonlinear Luttinger Liquid theory also predicts the correct dynamics at low energies, where it agrees with the conventional Luttinger liquid. Moreover, at high energies, the wave packet dynamics reveals signatures of composite excitations containing two-particle bound states. Our results uncover a simple strategy to probe the nonlinear regime in time-resolved experiments in quantum wires and ultracold-atom platforms.