Exploring helical phases of matter in bosonic ladders

Abstract

Ladder models of ultracold atoms offer a versatile platform for the experimental and theoretical study of different phenomena and phases of matter linked to the interplay between artificial gauge fields and interactions. Strongly correlated helical states are known to appear for specific ratios of the particle and magnetic flux densities and they can often be interpreted as a one-dimensional limit of fractional quantum Hall states, thus being called pretopological. Their signatures, however, are typically hard to observe due to the small gaps characterizing these states. Here we investigate bosonic ladder models at filling factor ν = 1. Based on bosonization, renormalization group and matrix product state simulations we pinpoint two strongly correlated helical phases appearing at this resonance. We show that one of them can be accessed in systems with two-species hardcore bosons and on-site repulsions only, thus amenable for optical lattice experiments. Its signatures are sizable and stable over a broad range of parameters for realistic system sizes.

$\mathbb{Z}_N$ lattice gauge theory in a ladder geometry

“…In the following we will consider C(r) to be suitably short-ranged; for a sharp momentum cutoff, C(r) ≈ J 0 (Λr) and this assumption is not satisfactorily fulfilled; however, C(r) can be made sufficiently short-ranged with more refined cutoffs [83,84].…”