Current quantization and fractal hierarchy in a driven repulsive lattice gas

TL;DR

This paper investigates a driven lattice gas with long-range repulsive interactions, revealing a fractal hierarchy of excitations, quantized current phases, and a transition between insulating and conducting states, highlighting complex non-equilibrium phenomena.

Contribution

It introduces a novel analysis of driven lattice gases with slow-decayed interactions, uncovering fractal hierarchies and quantized current phases not seen in nearest-neighbor models.

Findings

Identified an abrupt transition from insulating to conducting states.

Discovered current quantization into discrete phases.

Revealed a fractal hierarchy of excitations related to Farey sequences.

Abstract

Driven lattice gases are widely regarded as the paradigm of collective phenomena out of equilibrium. While such models are usually studied with nearest-neighbor interactions, many empirical driven systems are dominated by slowly decaying interactions such as dipole-dipole and Van der Waals forces. Motivated by this gap, we study the non-equilibrium stationary state of a driven lattice gas with slow-decayed repulsive interactions at zero temperature. By numerical and analytical calculations of the particle current as a function of the density and of the driving field, we identify (i) an abrupt breakdown transition between insulating and conducting states, (ii) current quantization into discrete phases where a finite current flows with infinite differential resistivity, and (iii) a fractal hierarchy of excitations, related to the Farey sequences of number theory. We argue that the origin of these effects is the competition between scales, which also causes the counterintuitive phenomenon that crystalline states can melt by increasing the density.