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arXiv:0712.2504 · Physical Review B

Quantum Monte Carlo study of a two-species bosonic Hubbard model

Siegfried Guertler, Matthias Troyer, Fu‐Chun Zhang

Published May 8, 2008• 11 citations
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Abstract

We consider a two-species hard-core boson Hubbard model for a supersolid, where two types of bosons represent vacancies and interstitials doped into a commensurate crystal. The on-site interspecies interaction can create bound states of vacancies and interstitials facilitating vacancy condensation at lower energies than in a single-species model, as suggested in an earlier mean-field study. Here, we carry out quantum Monte Carlo simulations to study possible supersolid phases of the model, which correspond to superfluid phases of the vacancies or interstitials. At low temperatures, we find three distinct superfluid phases. The extent of the phases and the nature of the phase transitions are discussed in comparison to mean-field theory.

DOI
10.1103/physrevb.77.184505

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We consider a two-species hard-core boson Hubbard model for a supersolid, where two types of bosons represent vacancies and interstitials doped into a commensurate crystal. The on-site interspecies interaction can create bound states of vacancies and interstitials facilitating vacancy condensation at lower energies than in a single-species model, as suggested in an earlier mean-field study. Here, we carry out quantum Monte Carlo simulations to study possible supersolid phases of the model, which correspond to superfluid phases of the vacancies or interstitials. At low temperatures, we find three distinct superfluid phases. The extent of the phases and the nature of the phase transitions are discussed in comparison to mean-field theory.
Using worm-type quantum Monte Carlo simulations, we investigate bosonic mixtures on a triangular lattice of two species of bosons, which interact via nearest-neighbor intraspecies (VVV) and on-site interspecies (UUU) repulsions. For the case of symmetric hopping amplitude (tA/V=tB/V{t}_{A}/V={t}_{B}/VtA​/V=tB​/V) and U/V=1U/V=1U/V=1, we determine a rich ground-state phase diagram that contains double-solid, double-superfluid, supersolid (SS), solid-superfluid (solid-SF), and counterflow supersolid (CSS) states. The SS, solid-SF, and CSS states exhibit spontaneous symmetry breaking among the three sublattices of the triangular lattice and between the two species, which leads to a nonzero crystalline density wave order in each species. We, furthermore, show that the CSS and the SS states are present for ${t}_{A}/V\ensuremath{\ne}{t}_{B}/V$, and the latter even survives up to the ${t}_{A}/V\ensuremath{\rightarrow}\ensuremath{\infty}$ or ${t}_{B}/V\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. The effects induced by the variation of U/VU/VU/V and by the imbalance of particle numbers of the two species are also explored.
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.
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 study a doped two-dimensional bosonic Hubbard model with two hard-core species using quantum Monte Carlo simulations. With doping we find five distinct phases, including a normal liquid at higher temperature, an antiferromagnetically ordered Mott insulator, a region of coexistent antiferromagnetic and superfluid phases near half filling, and farther away from half filling, a superfluid phase and a phase-separated ferromagnet. In the latter, the heavy species has Mott behavior with integer fillings, while the light species shows Mott and superfluid behaviors. The global entropy of this phase is relatively high which may provide a new avenue to obtain a polarized phase or a Mott insulator in cold-atom experiments.
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.
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.