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arXiv:1412.2245 · Physical Review B

Valence bond supersolid in a bilayer extended Bose-Hubbard model

Kwai-Kong Ng

Published Feb 23, 2015• 7 citations
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Abstract

The hardcore extended Bose Hubbard model on a bilayer square lattice with attractive (repulsive) interplane (intraplane) interactions has been investigated numerically. Focusing on the strong interplane hopping parameter regime, triplet valence bonds of dimers are stabilized to form valence bond checkerboard solid at quarter filling. Increasing the particle number we confirm the presence of the exotic valence bond supersolid phase, where the valence bond solid ordering and the boson superfluidity coexist. Rising further the particle number will lead to a checkerboard solid of dimer pair at half filling for strong intraplane repulsion, or a valence bond Mott insulator for weak repulsive interactions. We analyze the rich ground state phase diagrams of this model, which can be experimentally realized in optical lattices of cold atoms.

DOI
10.1103/physrevb.91.054516

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The hardcore extended Bose Hubbard model on a bilayer square lattice with attractive (repulsive) interplane (intraplane) interactions has been investigated numerically. Focusing on the strong interplane hopping parameter regime, triplet valence bonds of dimers are stabilized to form valence bond checkerboard solid at quarter filling. Increasing the particle number we confirm the presence of the exotic valence bond supersolid phase, where the valence bond solid ordering and the boson superfluidity coexist. Rising further the particle number will lead to a checkerboard solid of dimer pair at half filling for strong intraplane repulsion, or a valence bond Mott insulator for weak repulsive interactions. We analyze the rich ground state phase diagrams of this model, which can be experimentally realized in optical lattices of cold atoms.
We consider a minimal model to investigate the quantum phases of hardcore, polarized dipolar atoms confined in multilayer optical lattices. The model is a variant of the extended Bose-Hubbard model, which incorporates intralayer repulsion and interlayer attraction between the atoms in nearest-neighbor sites. We study the phases of this model emerging from the competition between the attractive interlayer interaction and the interlayer hopping. Our results from the analytical and cluster-Gutzwiller mean-field theories reveal that multimer formation occurs in the regime of weak intra- and interlayer hopping due to the attractive interaction. In addition, intralayer isotropic repulsive interaction results in the checkerboard ordering of the multimers. This leads to an incompressible checkerboard multimer phase at half-filling. At higher interlayer hopping, the multimers are destabilized to form resonating valence-bond-like states. Furthermore, we discuss the effects of thermal fluctuations on the quantum phases of the system.
The stability of the supersolid state of bosons reported recently on the checkerboard lattice in the vicinity of a valence-bond crystal phase is assessed. In contrast to previously identified supersolid phases of lattice bosons, this state would---if stable---provide superfluidity atop a solid with inherent quantum dynamics, restricted to the particular filling fraction of one quarter. Using large-scale quantum Monte Carlo simulations based on the stochastic series expansion method constrained to the canonical ensemble, the supersolid state is, however, found to be unstable in the thermodynamic limit. Converging crossing points in both the winding number fluctuations and the Binder ratio related to the order parameter of the valence-bond crystal instead exhibit a direct quantum melting transition of the crystal into the superfluid regime.
We study the ground-state properties of the extended Bose-Hubbard model in a one-dimensional dimerized optical lattice. In the limit of strong on-site repulsion, i.e., hardcore bosons, and strong nearest-neighbor interaction, a stable density-wave (DW) phase is obtained at half-filling as a function of lattice dimerization. Interestingly, at quarter-filling we obtain the signatures of an insulating phase which has the character of both the bond order (BO) and the DW insulators, which we call a bond-order density-wave (BODW) phase. Moreover, we show that for a fixed hopping dimerization there occurs a BO-DW phase crossover as a function of the nearest-neighbor interaction and the BODW phase is more robust when the hopping dimerization is stronger. We further examine the stability of the BODW phase in the limit of finite on-site interactions.
By using the inhomogeneous mean-field theory, the phase diagram of the two-dimensional soft-core extended Bose-Hubbard model with both on-site and nearest-neighbor interactions in the presence of spatial disorder is determined. Rich phases, including Mott-insulator, checkerboard solid, supersolid, superfluid and disordered solid are obtained. Interestingly, due to the presence of disorder, a new disordered solid phase is found between the incompressible lobes, and it is demonstrated that the supersolid phase can survive in two-dimensional soft-core bosons. Furthermore, the system undergoes the phase transition from a disordered solid into a solid order or supersolid landscape when the disorder strength is increased. For weak nearest-neighbor repulsion, the increase of the disorder strength induces both checkerboard solid and supersolid phases shrinking to smaller hopping regions. However, for strong nearest-neighbor repulsion, the disorder stabilizes the supersolid phase and makes it occupying a remarkably broad region in the phase diagram. The analytical expressions for the phase boundaries between the incompressible and compressible phases are also obtained, which are in qualitative agreement with our numerical results.
By using a state-of-the-art tensor network state method, we study the ground-state phase diagram of an extended Bose-Hubbard model on the square lattice with frustrated next-nearest-neighbor tunneling. In the hard-core limit, tunneling frustration stabilizes a peculiar half-supersolid phase with one sublattice being superfluid and the other sublattice being Mott insulator away from half filling. In the soft-core case, the model shows very rich phase diagrams above half filling, including three different types of supersolid phases depending on the interaction parameters. The considered model provides a promising route to experimentally search for a novel stable supersolid state induced by frustrated tunneling in the region below half filling with dipolar atoms or molecules.
We investigate the ground-state phase diagram of a two-component extended Bose-Hubbard model recently realized with dipolar excitons, using the projected entangled-pair states. For the experimentally relevant parameter regime, checkerboard, Mott-insulating, superfluid, and vacuum phases are identified. These phases exhibit orbital-selective character, wherein the two components occupy different quantum states, but we find no evidence for a supersolid phase. The absence of supersolidity is attributed to the strongly interaction-dominated microscopic energy scales, which severely restrict the superfluid regime. Guided by the supersolid mechanism, we further explore a nearby parameter regime with enhanced hopping of one component and identify an orbital-selective supersolid phase. Further finite bond-dimension and unit-cell analyses establish the robustness of this phase. Our results clarify the zero-temperature phase structure of the dipolar-exciton platform and provide a possible route toward realizing supersolidity in this setting.