Abstract
Helical liquids have been experimentally realized in both nanowires and ultracold atomic chains as the result of strong spin–orbit interactions. In both cases the inner degrees of freedom can be considered as an additional space dimension, providing an interpretation of these systems as chiral synthetic ladders, with artificial magnetic fluxes determined by the spin–orbit terms. In this work, we characterize the helical state which appears at filling ν = 1/2: this state is generated by a gap arising in the spin sector of the corresponding Luttinger liquid and it can be interpreted as the one-dimensional (1D) limit of a fractional quantum Hall state of bosonic pairs of fermions. We study its main features, focusing on entanglement properties and correlation functions. The techniques developed here provide a key example for the study of similar quasi-1D systems beyond the semiclassical approximation commonly adopted in the description of the Laughlin-like states.
Highlights
The scientific paradigm of topological phases of matter lays its foundation on the experimental engineering of solid state devices ranging from topological insulators and superconductors [1] to fractional quantum Hall (FQH) setups [2]
The striding evolution of this field is progressively investing a variegated plethora of other platforms and, among them, ultracold atoms trapped in optical lattices [3] offered an unprecedented scenario for the direct implementations of toy-models, such as the Hofstadter [4,5,6] or Haldane [7] models, which play a key role in our understanding of the topological phenomena in condensed matter physics
One of the most appealing developments in this field is based on the idea of synthetic dimensions [8]: the inner degrees of freedom of the trapped atoms can represent an additional physical dimension and, in this scenario, the introduction of a laser-induced spin–orbit coupling is translated into large magnetic fluxes in the synthetic lattice [9]
Summary
In both cases the inner degrees of freedom can be considered. The spin sector of the corresponding Luttinger liquid and it can be interpreted as the one-dimensional (1D) limit of a fractional quantum Hall state of bosonic pairs of fermions. The techniques developed here provide a key example for the study of similar quasi-1D systems beyond the semiclassical approximation commonly adopted in the description of the Laughlin-like states
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