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arXiv:0803.1116 · Physical Review B

Vacancy supersolid of hard-core bosons on the square lattice

Long Dang, Massimo Boninsegni, Lode Pollet

Published Oct 29, 2008• 46 citations
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Abstract

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.

DOI
10.1103/physrevb.78.132512

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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 \ensuremathρ<0.25\ensuremath{\rho}<0.25\ensuremathρ<0.25. At filling \ensuremathρ>0.25\ensuremath{\rho}>0.25\ensuremathρ>0.25, a supersolid phase exists between the star and the stripe crystal at \ensuremathρ=0.5\ensuremath{\rho}=0.5\ensuremathρ=0.5. No supersolid phase occurs for \ensuremathρ>0.25\ensuremath{\rho}>0.25\ensuremathρ>0.25 if the ground state at half-filling is either a checkerboard crystal or a superfluid. No commensurate supersolid phase is observed.
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 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.
We determine the phase diagram of hard-core bosons on a triangular lattice with nearest-neighbor repulsion, paying special attention to the stability of the supersolid phase. Similar to the same model on a square lattice we find that for densities rho<1/3 or rho>2/3 a supersolid phase is unstable and the transition between a commensurate solid and the superfluid is of first order. At intermediate fillings 1/3<rho<2/3 we find an extended supersolid phase even at half filling rho=1/2. The emergence of the supersolid on the triangular lattice reflects a novel and interesting way for a quantum system to avoid classical frustration, similar to an order-by-disorder mechanism. It also offers an exciting possibility of realizing such phenomena in ultracold atoms on optical lattices.
We study the ground-state properties of repulsively interacting bosons on the honeycomb lattice using large-scale quantum Monte Carlo simulations. In the hard-core limit, the half-filled system develops long-ranged diagonal order for sufficiently strong nearest-neighbor repulsion. This staggered solid melts at a first-order quantum phase transition into the superfluid phase, without the presence of any intermediate supersolid phase. Within the superfluid phase, both the superfluid density and the compressibility exhibit local minima near the particle (hole) density of one quarter, while the density and the condensate fraction show inflection points in this region. Relaxing the hard-core constraint, supersolid phases emerge for soft-core bosons. The suppression of the superfluid density is found to persist for sufficiently large, finite on-site repulsion.
Understanding the microscopic mechanism of coexisting long-range orders (such as lattice supersolidity) in strongly correlated systems is a subject of immense interest. We study the possible manifestations of long-range orders, including lattice-supersolid phases with differently broken symmetry, in a two-dimensional square lattice system of hard-core bosons (HCBs) coupled to archetypal cooperative/coherent normal-mode distortions such as those in perovskites. At strong HCB-phonon coupling, using a duality transformation to map the strong-coupling problem to a weak-coupling one, we obtain an effective Hamiltonian involving nearest-neighbor, next-nearest-neighbor, and next-to-next-nearest-neighbor hoppings and repulsions. Using stochastic series expansion quantum Monte Carlo, we construct the phase diagram of the system. As coupling strength is increased, we find that the system undergoes a first-order quantum phase transition from a superfluid to a checkerboard solid at half-filling and from a superfluid to a diagonal striped solid [with crystalline ordering wave vector $\stackrel{P\vec}{Q}=(2\ensuremath{\pi}/3,2\ensuremath{\pi}/3)$ or $(2\ensuremath{\pi}/3,4\ensuremath{\pi}/3)]$ at one-third filling without showing any evidence of supersolidity. On tuning the system away from these commensurate fillings, checkerboard supersolid is generated near half-filling whereas a rare diagonal striped supersolid is realized near one-third filling. Interestingly, there is an asymmetry in the extent of supersolidity about one-third filling. Within our framework, we also provide an explanation for the observed checkerboard and stripe formations in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4}$ at x=1/2x=1/2x=1/2 and x=1/3x=1/3x=1/3.