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arXiv:0708.1807 · Physical Review B

Supersolidity from defect condensation in the extended boson Hubbard model

Yi‐Chun Chen, Roger G. Melko, Stefan Weßel, Ying-Jer Kao

Published Jan 28, 2008• 57 citations
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Abstract

We study the ground-state phase diagram of the hard-core extended boson Hubbard model on the square lattice with both nearest- and next-nearest-neighbor hoppings and repulsions, using Gutzwiller mean-field theory and quantum Monte Carlo simulations. We observe the formation of supersolid states with checkerboard, striped, and quarter-filled crystal structures when the system is doped away from commensurate fillings. In the striped supersolid phase, a strong anisotropy in the superfluid density is obtained from the simulations; however, the transverse component remains finite, indicating a true two-dimensional superflow. We find that upon doping, the striped supersolid transitions directly into the supersolid with quarter-filled crystal structure, via a first-order stripe melting transition.

DOI
10.1103/physrevb.77.014524

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We study the ground-state phase diagram of the hard-core extended boson Hubbard model on the square lattice with both nearest- and next-nearest-neighbor hoppings and repulsions, using Gutzwiller mean-field theory and quantum Monte Carlo simulations. We observe the formation of supersolid states with checkerboard, striped, and quarter-filled crystal structures when the system is doped away from commensurate fillings. In the striped supersolid phase, a strong anisotropy in the superfluid density is obtained from the simulations; however, the transverse component remains finite, indicating a true two-dimensional superflow. We find that upon doping, the striped supersolid transitions directly into the supersolid with quarter-filled crystal structure, via a first-order stripe melting transition.
The ground state of hard-core bosons on the square lattice with nearest and next-nearest-neighbor repulsion is studied by quantum Monte Carlo simulations. A supersolid phase with vacancy condensation and ``star'' diagonal ordering is found for filling $\ensuremath{\rho}<0.25$. At filling $\ensuremath{\rho}>0.25$, a supersolid phase exists between the star and the stripe crystal at $\ensuremath{\rho}=0.5$. No supersolid phase occurs for $\ensuremath{\rho}>0.25$ if the ground state at half-filling is either a checkerboard crystal or a superfluid. No commensurate supersolid phase is observed.
We present a comprehensive numerical study on the ground state phase diagram of the two-dimensional hard core bosonic extended Hubbard model with nearest (V1)({V}_{1})(V1​) and next nearest neighbor (V2)({V}_{2})(V2​) repulsions. In addition to the quantum solid and superfluid phases, we report the existence of a striped supersolid and three-quarter (quarter)-filled supersolid at commensurate density $\ensuremath{\rho}=0.75$ (0.25) due to the interplay of V1{V}_{1}V1​ and V2{V}_{2}V2​ interactions. The nature of the three-quarter-filled supersolid and the associated quantum solid will be discussed. The observed quantum phase transition between the two supersolids of different symmetries is found to be first order.
Using an unbiased quantum Monte Carlo method, we obtain convincing evidence of the existence of a checkerboard supersolid at a commensurate filling factor 1/2 (a commensurate supersolid) in the soft-core Bose-Hubbard model with nearest-neighbor repulsions on a cubic lattice. In conventional cases, supersolids are realized at incommensurate filling factors by a doped-defect-condensation mechanism, where particles (holes) doped into a perfect crystal act as interstitials (vacancies) and delocalize in the crystal order. However, in the model, a supersolid state is stabilized even at the commensurate filling factor 1/2 without doping. By performing grand canonical simulations, we obtain a ground-state phase diagram that suggests the existence of a supersolid at a commensurate filling. To obtain direct evidence of the commensurate supersolid, we next perform simulations in canonical ensembles at a particle density ρ=1/2 and exclude the possibility of phase separation. From the obtained snapshots, we discuss its microscopic structure and observe that interstitial-vacancy pairs are unbound in the crystal order.
We numerically study the ground state phase diagram of the two-dimensional hard-core Bose-Hubbard model with nearest-(V(1)) and next-nearest-neighbour (V(2)) repulsions. In particular, we focus on the quarter-filled phases where one supersolid and two solid phases are observed. Using both canonical and grand canonical quantum Monte Carlo (QMC) methods and a mean-field calculation, we provide evidence for the existence of a commensurate supersolid. Despite the two possible diagonal long-range orderings for the solid phase, only one kind of supersolid phase is found to be energetically stable. The competition between the two solid phases manifests itself as a first-order phase transition around 2V(2) ∼ V(1). The change of order parameters as a function of the chemical potential is also presented.
We investigate numerically the finite-temperature phase diagrams of the extended Bose-Hubbard model in a two-dimensional square lattice. In particular, we focus on the melting of supersolid phases of two different crystal orderings, stripe and star orders, arising from the competition of the nearest- and next-nearest-neighbor interactions in the vicinity of quarter filling. The two crystal orders are the result of broken translational symmetry in either one or in both xxx and yyy directions. The broken gauge symmetry of the supersolids are found to be restored via a Kosterlitz-Thouless transition while the broken translational symmetries are restored via a single second-order phase transition, instead of two second-order transitions in the Ising universality class. On the other hand, the phase transitions between the star and stripe orders are first order in nature.
We investigate the ground-state phase diagram of the soft-core Bose-Hubbard model with the nearest-neighbor repulsion on a square lattice by using an unbiased quantum Monte Carlo method. In contrast to a previous study [P. Sengupta et al., Phys. Rev. Lett. 94, 207202 (2005)], we present the ground-state phase diagrams up to high hopping amplitudes. As a result, in addition to the known supersolid above half-filling, we find a supersolid phase below and at half-filling for high hopping amplitudes. In addition, for a strong nearest-neighbor repulsion, we show that the supersolid phase occupies a remarkably broad region in the phase diagram. These results are in agreement with the results of the Gutzwiller mean-field approximation [M. Iskin, Phys. Rev. A 83, 051606(R) (2011); T. Kimura, Phys. Rev. A 84, 063630 (2011)]. However, it turns out that the regions of the supersolid phases are significantly smaller than the mean-field results.