Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

TL;DR

This paper investigates various symmetry-breaking quantum phases of interacting bosons on a two-leg ladder with a uniform gauge field, revealing new vortex-lattice and charge-density-wave states, their transitions, and experimental signatures.

Contribution

It provides a comprehensive analysis of symmetry-broken states in this system, including vortex lattices and charge-density waves, using DMRG simulations and analytical methods, with relevance to experiments.

Findings

Identification of three vortex-lattice states at different densities

Characterization of phase transitions between vortex states and neighboring phases

Analytical description of phase boundaries and experimental signatures

Abstract

We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex-fluids, vortex-lattices, charge-density-waves and the biased-ladder phase. Our work focuses on the subset of these states that break a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux-quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact to recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.