Crossover from Wannier-Stark localization to charge density waves for interacting spinless fermions in one dimension

TL;DR

This paper investigates how spinless fermions in one dimension transition from Wannier-Stark localization to charge density wave states under varying electric fields and interactions, combining analytical and numerical methods.

Contribution

It provides analytical expressions for localization length and explores the evolution of charge density profiles and spectra with interaction strength and electric field.

Findings

Localization length is inversely proportional to electric field.

Charge density wave forms in the intermediate region for strong interactions.

Spectrum shows Wannier-Stark ladder structure that smears out with strong interactions.

Abstract

We study spinless fermions on a finite chain with nearest-neighbor repulsion and in the presence of a Wannier-Stark linearly-varying electric field potential. In the absence of the interaction, the eigenstates are localized for the system's sizes larger than the localization length. We present several analytical expressions for the localization length, which is proportional to the inverse of the electric field. Using the density matrix renormalization group numerical technique, we observe that the ground state exhibits a decrease of the occupation on the chain sites from the `bulk', with occupation 1, to the vacuum, with occupation 0. The width of this intermediate `edge' region is also inversely proportional to the electric field, increasing linearly with the strength of the nearest-neighbor repulsion. For strong interactions, the occupations in the intermediate region exhibit a charge density wave. We also present the local density of states for sites in the `edge' region. For the non-interacting case, the spectrum shows an increasing energy-localized structure as the field is increased, which is a consequence of the uniform energy distribution of the localized states (Wannier-Stark ladder). This structure survives for small interactions, and it smears out in the strongly interacting limit. Experimental variations of the slope of the potential (the electric field) on cold atom chains may test these predictions.