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arXiv:1505.06958 · Physical review. B./Physical review. B

Exotic Haldane superfluid phase of soft-core bosons in optical lattices

Jian-Ping Lv, Z. D. Wang

Published May 13, 2016• 5 citations
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Abstract

We propose to realize an exotic Haldane superfluid (HSF) phase in an extended Bose-Hubbard model on the two-leg ladder (i.e., a two-species mixture of interacting bosons). The proposal is confirmed by means of large-scale quantum Monte Carlo simulations, with a significant part of the ground-state phase diagram being revealed. Most remarkably, the newly discovered HSF phase features both superfluidity and nonlocal topological Haldane order. The effects induced by varying the number of legs are furthermore explored. Our results shed light on how topological superfluid emerges in bosonic systems.

DOI
10.1103/physrevb.93.174507

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We propose to realize an exotic Haldane superfluid (HSF) phase in an extended Bose-Hubbard model on the two-leg ladder (i.e., a two-species mixture of interacting bosons). The proposal is confirmed by means of large-scale quantum Monte Carlo simulations, with a significant part of the ground-state phase diagram being revealed. Most remarkably, the newly discovered HSF phase features both superfluidity and nonlocal topological Haldane order. The effects induced by varying the number of legs are furthermore explored. Our results shed light on how topological superfluid emerges in bosonic systems.
We study the extended Bose-Hubbard model on a two-dimensional honeycomb lattice by using large-scale quantum Monte Carlo simulations. We present the ground-state phase diagrams for both the hard-core and the soft-core bosons. For the hard-core case, the transition between the $\ensuremath{\rho}=1∕2$ solid and the superfluid is first order, and the supersolid state is unstable toward phase separation. For the soft-core case, due to the presence of multiple occupation, a stable particle-induced supersolid (SS-p) phase emerges when $1∕2<\ensuremath{\rho}<1$. The transition from the solid at $\ensuremath{\rho}=1∕2$ to the SS-p phase is second order with the superfluid density scaling as ${\ensuremath{\rho}}_{s}\ensuremath{\sim}\ensuremath{\rho}\ensuremath{-}1∕2$. The SS-p phase has the same diagonal order as the solid at $\ensuremath{\rho}=1∕2$. As the chemical potential increases further, the SS-p phase turns into a solid where two bosons occupy each site of one sublattice through a first-order transition. We also calculate the critical exponents of the transition between the $\ensuremath{\rho}=1∕2$ solid and superfluid at the Heisenberg point for the hard-core case. We find the dynamical critical exponent z=0.15z=0.15z=0.15, which is smaller than results obtained on smaller lattices. This indicates that zzz approaches zero in the thermodynamic limit, and thus the transition is also first order even at the Heisenberg point.
The Haldane insulator is a gapped phase characterized by an exotic nonlocal order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understood. Using the stochastic Green function quantum Monte Carlo algorithm and density matrix renormalization group, we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves, superfluid, supersolid, and the recently identified Haldane insulating phases. We show that the Haldane insulating phase exists only at the tip of the unit-filling charge density wave lobe and that there is a stable supersolid phase over a very wide range of parameters.
The Haldane phase (HP) is a paradigmatic example of symmetry protected topological phase. We explore how the bosonic HP behaves in the presence of local disorder, employing quantum Monte Carlo simulations of an extended Bose-Hubbard model subject to uncorrelated, quenched disorders. We find that the HP is robust against a weak disorder and the non-local string order of HP exhibits a reentrant behavior. Besides, a direct transition between the HP and superfluid phase is uncovered. A significant part of the ground-state phase diagram is established for the model, unveiling the location of HP surrounded by Bose glass, charge-density-wave–like and superfluid phases. We also mention a possible experimental scheme with optical lattice emulator to realize the present findings.
We investigate the ground-state properties of a newly discovered phase of one-dimensional lattice bosons with extended interactions [E. G. Dalla Torre et al., Phys. Rev. Lett. 97, 260401 (2006)]. The new phase, termed the Haldane insulator in analogy with the gapped phase of spin-1 chains, is characterized by a nonlocal order parameter, which can only be written as an infinite string in terms of the bosonic densities. We show that the string order can nevertheless be probed with physical fields that couple locally, via the effect those fields have on the quantum phase transitions separating the exotic phase from the conventional Mott and density wave phases. Using a field theoretical analysis, we show that a perturbation that breaks lattice inversion symmetry gaps the critical point separating the Mott and Haldane phases and eliminates the sharp distinction between them. This is remarkable given that neither of these phases involves broken inversion symmetry. We also investigate the evolution of the phase diagram with the tunable coupling between parallel chains in an optical lattice setup. We find that interchain tunneling destroys the direct phase transition between the Mott and Haldane insulators by establishing an intermediate superfluid phase. On the other hand, coupling the chains only by weak repulsive interactions does not modify the structure of the phase diagram. The theoretical predictions are confirmed with numerical calculations using the density matrix renormalization group.
We study the topological properties of an extended Bose-Hubbard model with cyclically modulated hopping and on-site potential parameters, which can be realized with ultracold bosonic atoms in a one-dimensional optical superlattice. We show that the interacting bosonic chain at half filling and in the deep Mott insulating regime can simulate bosonic Chern insulators with a topological phase diagram similar to that of the Haldane model of noninteracting fermions. Furthermore, we explore the topological properties of the ground state by calculating the many-body Chern number, the quasiparticle energy spectrum with gapless edge modes, the topological pumping of the interacting bosons, and the topological phase transition from normal (trivial) to topological Mott insulators. We also present the global phase diagram of the many-body ground state, which contains a superfluid phase and two Mott insulating phases with trivial (a zero Chern number) and nontrivial topologies (a nonzero Chern number), respectively.
We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and nonlocal terms gives rise to a phase diagram with liquid phases with dominant cluster, spin-, and density-wave quasi-long-range ordering. These phases are separated by Berezinskii-Kosterlitz-Thouless, Gaussian, and supersymmetric (SUSY) quantum critical transitions. For the latter, we provide a phenomenological description of coupled SUSY conformal field theories, whose predictions are confirmed by matrix product state simulations. Our results are motivated by, and directly relevant to, recent experiments with Rydberg-dressed atoms in optical lattices, where ladder dynamics has already been demonstrated, and emphasize the capabilities of these setups to investigate exotic quantum phenomena such as cluster liquids and coupled SUSY conformal field theories.