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 breaks 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 with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.

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

“…In Ref. [56], an incommensurate Meissner phase has been observed numerically for density an 0 = 0.4 at flux aχ/(2π ) = 0.4, which belongs to the precursor-to-Laughlin state region on our phase diagram. The study in Ref.…”

“…Vortex lattice states, in which the discrete lattice translation symmetry is spontaneously broken, exist for U finite [55]. The two-leg ladder has other such symmetry broken states: charge density waves, as well as the biased ladder state which breaks the symmetry between the two chains [56].…”

Vortex-Hole Duality: A Unified Picture of Weak- and Strong-Coupling Regimes of Bosonic Ladders with Flux

“…Table I summarizes the weak and strong-coupling duality relations. In the weak coupling regime of bosonic ladders few VL superfluids were observed [3,4] to survive quantum fluctuations on top of the classical Josephson-junction (JJ) limit [5]. A vortex in the classical JJ limit, where the phase at each ladder site has definite value, carries a quantum of a fluxoid and is localized on …”

“…simulations of a Bose-Hubbard model on a two-leg ladder with flux showed that particle densities get depleted in the plaquettes where vortices sit, when including quantum fluctuations, and topological excitations of the VL states are domain walls, carrying fractional fluxoids [3,4]. Contact-interacting cold quantum gases loaded in onedimensional lattices, with an additional second "synthetic" dimension, can explore this duality in the presence of a homogeneous gauge field.…”

“…Since all particles on the same synthetic dimensional rung share the same optical lattice site, contact interactions lead to exotic long-ranged interactions along the rungs, which for typical systems [10,11] may be assumed to be SUðMÞ symmetric. The interplay of long-ranged interactions along the synthetic dimension and homogeneous gauge fields has attracted considerable attention recently, as it gives rise to the ground states bearing analogies with quantum Hall-like behavior [13][14][15][16][17][18][19][20][21], or exhibiting exotic quantum magnetism [4,18,[22][23][24][25][26][27][28][29][30][31].…”