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

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.

25 pages, 26 figures

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• Snapshot based characterization of particle currents and the Hall response in synthetic flux lattices
• Realization of strongly-interacting Meissner phases in large bosonic flux ladders
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• Finite-temperature properties of interacting bosons on a two-leg flux ladder
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• Effective triangular ladders with staggered flux from spin-orbit coupling in 1D optical lattices
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• Neural-network quantum states for a two-leg Bose-Hubbard ladder under magnetic flux
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• Interaction-induced exotic vortex states in an optical lattice clock with spin-orbit coupling
• Quantum simulation of the tricritical Ising model in tunable Josephson junction ladders
• Flux enhanced localization and reentrant delocalization in the quench dynamics of two interacting bosons on a Bose-Hubbard ladder
• Flux induced re-entrant dynamics in the quantum walk of interacting bosons
• Quantum phases of constrained bosons on a two-leg Bose-Hubbard ladder
• Meissner effect in Fock space
• Current jumps in flat band ladders with Dzyaloshinskii-Moriya interactions
• Interaction-induced chiral-transport inversion
• $Z_2\times Z_2$ symmetry and $Z_4$ Berry phase of bosonic ladder
• Engineering a Josephson junction chain for the simulation of the clock model
• Absence of gapless Majorana edge modes in few-leg bosonic flux ladders