Chiral currents in one-dimensional fractional quantum Hall states

Abstract

We study bosonic and fermionic quantum two-leg ladders with orbital magnetic flux. In such systems, the ratio, ν, of particle density to magnetic flux shapes the phase-space, as in quantum Hall effects. In fermionic (bosonic) ladders, when ν 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 ν, 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.

Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

“…5. We attribute this discrepancy to the neglect of Fermi sea contributions in the bosonization treatment, in agreement with a recent analytical argument for the ν = 1 integer quantum Hall state in the same geometry [40].…”

“…Recent investigations into fermions on the simplest geometry of two-leg ladders (i.e., systems composed of two coupled Luttinger liquids) satisfying filling fraction ν = 1/m (m = 1,3,...) reveal that the topological phase on the ladder is manifest in local observables, such as singularities in the dependence of antisymmetric chiral current on flux [40]. We pursue in this paper the analogous problem of a tight-binding model of hard-core particles with bosonic statistics at arbitrary filling and in uniform flux.…”

Crystallization of fractional charges in a strongly interacting quasihelical quantum dot

“…This splitting can be suggestively interpreted as the crystallization of (2n + 1)N 0 fractional quasi-particles, with fractional charge e/(2n + 1), which tend to distribute evenly in space in order to minimize the strong repulsive interactions giving rise to N p distinct peaks in the density. It is very interesting to observe that, although several predictions have been already made concerning fractional excitations in strongly interacting spin-orbit coupled wires in the presence of a magnetic field 18,19,21,22 , in this work we predict that a bulk ground-state propertythe density ρ(x) -exhibits signatures of these fractional quasi-particles.…”

“…This would not only allow to confirm the predictions made here concerning the fixed point of the theory, but also in principle to observe the transition towards the crystal of fractional quasi-particles. In a recent paper 22 it has been shown that for V (n) Z,7/8 to be relevant at n ≥ 1, on-site repulsion (however strong) is not sufficient in the Hubbard model 38 . This seems to imply that a non-zero range interaction is needed to observe the predicted effects.…”

“…They are accompanied by several signatures, such as the occurrence of low-energy excitations with fractional charge 18,19 which induce a non-integer quantization of the conductance [18][19][20] . Also the shot noise becomes fractionalized 21 and unusual properties of the chiral currents have been reported very recently 22 .…”