Chiral currents in one-dimensional fractional quantum Hall states

TL;DR

This paper investigates fractional quantum Hall states in two-leg ladder systems with magnetic flux, identifying unique chiral current signatures that depend on particle density and flux, and proposing experimental tests.

Contribution

It demonstrates the stabilization of Laughlin FQH states at specific fractional fillings in bosonic and fermionic ladders with long-range interactions, linking these states to observable chiral current behaviors.

Findings

FQH states occur at specific fractional fillings in ladder systems.

Chiral currents exhibit unique dependence on density and flux for FQH states.

Results are applicable to ultracold atom experiments and related models.

Abstract

We study bosonic and fermionic quantum two-leg ladders with orbital magnetic flux. In such systems, the ratio, $\nu$, of particle density to magnetic flux shapes the phase-space, as in quantum Hall effects. In fermionic (bosonic) ladders, when $\nu$ equals one over an odd (even) integer, Laughlin fractional quantum Hall (FQH) states are stabilized for sufficiently long ranged repulsive interactions. As a signature of these fractional states, we find a unique dependence of the chiral currents on particle density and on magnetic flux. This dependence is characterized by the fractional filling factor $\nu$, and forms a stringent test for the realization of FQH states in ladders, using either numerical simulations or future ultracold-atom experiments. The two-leg model is equivalent to a single spinful chain with spin-orbit interactions and a Zeeman magnetic field, and results can thus be directly borrowed from one model to the other.