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arXiv:1610.02435 · Physical Review A

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

Sebastian Greschner, Marie Piraud, Fabian Heidrich‐Meisner, Ian P. McCulloch, Ulrich Schollwöck, T. Vekua

Published Dec 22, 2016• 82 citations
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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.

DOI
10.1103/physreva.94.063628

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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.
Motivated by experiments exploring the physics of neutral atoms in artificial magnetic fields, we study the ground state of bosons interacting with long-range dipolar interactions on a two-leg ladder. We focus on the limit where the number of particles per site is large and the interactions are weak. Using two complementary variational approaches, we find rich physics driven by the long-range forces. Generically, long-range interactions tend to destroy the Meissner phase in favor of modulated density wave phases. For example, nearest-neighbor interactions produce an interleg charge density wave phase, where the total density remains uniform but the density on each leg of the ladder is modulating in space, out of phase with one another. Next-nearest-neighbor interactions lead to a fully modulated biased ladder phase, where all of the particles are on one leg of the ladder. This state simultaneously breaks Z2{Z}_{2}Z2​ reflection symmetry and U(1)\mathrm{U}(1)U(1) translation symmetry. For values of the flux near $\ensuremath{\phi}=\ensuremath{\pi}$, we find a switching effect for arbitrarily weak interactions, where the density is modulated but the chiral current changes sign on every plaquette. Arbitrarily weak attractive interactions along the rungs destroy the Meissner phase completely, in favor of a modulated density wave phase. Remarkably, varying the rung to ladder hopping produces a cascade of first-order transitions between modulated density wave states with different wave vectors, which manifests itself as discrete jumps in the chiral current. Polarizing the dipoles along the ladder direction yields a region of phase space where a stable biased ladder phase occurs even at arbitrarily weak rung hopping. We discuss the experimental consequences of our work and draw connections between our work and recent experiments on cold atoms in synthetic dimensions.
We consider interacting bosonic particles on a two-leg triangular ladder in the presence of an artificial gauge field. We employ density matrix renormalization group numerical simulations and analytical bosonization calculations to study the rich phase diagram of this system. We show that the interplay between the frustration induced by the triangular lattice geometry and the interactions gives rise to multiple chiral quantum phases. Phase transitions between superfluid to Mott-insulating states occur, which can have Meissner or vortex character. Furthermore, a state that explicitly breaks the symmetry between the two legs of the ladder, the biased chiral superfluid, is found for values of the flux close to $\ensuremath{\pi}$. In the regime of hard-core bosons, we show that the extension of the bond order insulator beyond the case of the fully frustrated ladder exhibits Meissner-type chiral currents. We discuss the consequences of our findings for experiments in cold atomic systems.
We investigate hard-core bosons at half filling on a three-leg ladder under the uniform artificial gauge field. By analyzing current patterns and correlation functions, we uncover a rich quantum phase diagram containing multiple superfluid and insulating phases. In bosonic ladder systems, increasing the gauge flux typically destabilizes the Meissner phase and leads to vortex phases characterized by circulating currents. In the present system, however, we find that charge-density-wave (CDW) phases emerge precisely in such a flux regime despite the presence of only an on-site interaction, where vortex states are naturally expected and are indeed realized in nearby parameter regions. While part of this behavior can be qualitatively understood from a strong-coupling perspective, we also identify an isolated CDW region that cannot be connected to such limits. Furthermore, upon increasing the artificial gauge flux, we observe a reentrant sequence of quantum phase transitions, CDW →\to→ vortex-superfluid →\to→ CDW, revealing a strong competition between the vortex phase and the density-wave order.
We establish the phase diagram of the strongly interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by a recent experiment [M. Atala et al., Nat. Phys. 10, 588 (2014)], which studied the same system, in the complementary regime of weak interactions. Based on extensive density matrix renormalization group simulations and a bosonization analysis, we fully explore the parameter space spanned by filling, interleg tunneling, and flux. As a main result, we demonstrate the existence of gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes. We calculate experimentally accessible observables such as chiral currents and vortex patterns.
Flux ladders constitute the minimal setup enabling a systematic understanding of the rich physics of interacting particles subjected simultaneously to strong magnetic fields and a lattice potential. In this paper, the ground-state phase diagram of a flux-ladder model is mapped out using extensive density-matrix renormalization-group simulations. The emphasis is put on parameters which can be experimentally realized exploiting the internal states of potassium atoms as a synthetic dimension. The focus is on accessible observables such as the chiral current and the leg-population imbalance. Considering a particle filling of one boson per rung, we report the existence of a Mott-insulating Meissner phase as well as biased-ladder phases on top of superfluids and Mott insulators. Furthermore, we demonstrate that quantum quenches from suitably chosen initial states can be used to probe the equilibrium properties in the transient dynamics. Concretely, we consider the instantaneous turning on of hopping matrix elements along the rungs or legs in the synthetic flux-ladder model, with different initial particle distributions. We show that clear signatures of the biased-ladder phase can be observed in the transient dynamics. Moreover, the behavior of the chiral current in the transient dynamics is discussed. The results presented in this paper provide guidelines for future implementations of flux ladders in experimental setups exploiting a synthetic dimension.
We perform a density-matrix renormalization-group study of strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux. Focusing on one-third filling, we explore the phase diagram in dependence of the magnetic flux and the inter-leg tunneling strength. We find several phases including a Meissner phase, vortex liquids, a vortex lattice, as well as a staggered-current (SC) phase. Moreover, there are regions where the chiral current reverses its direction, both in the Meissner and in the SC phase. While the reversal in the latter case can be ascribed to spontaneous breaking of translational invariance, in the first it stems from an effective flux increase in the rung direction. Interactions are a necessary ingredient to realize either type of chiral-current reversal.