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Physical Review A

Interacting hard-core bosons with anisotropic hopping: Checkerboard supersolid, order by disorder, and first-order phase transitions

Huo Xiao, Yong-Yong Cui, Dali Wang, Jian-Ping Lv

Published Feb 14, 2017• 8 citations
Publisher

Abstract

Using extensive quantum Monte Carlo simulations, we study a minimum model of interacting hard-core bosons on a square lattice with hoppings of different lengths, featuring nearest-neighbor hopping (${t}_{1}$), anisotropic next-nearest-neighbor hopping (${t}_{2}^{\ensuremath{'}}$), and nearest-neighbor repulsion (${V}_{1}$). The paradigmatic checkerboard supersolid (CSS) phase emerges as ${t}_{2}^{\ensuremath{'}}$ turns on, with the solid order being characterized by ordering vector $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$. This serves as a rare example of the CSS phase which is obtained by doping a checkerboard solid and harbors spontaneously broken gauge and translational symmetries. A first-order supersolid-to-superfluid transition is observed. Moreover, we find a solid order-by-thermal disorder behavior together with a superfluid-to-solid transition upon increasing temperature. The underlying picture of the order-by-disorder phenomenon is figured out within the framework of the entropy effect.

DOI
10.1103/physreva.95.023613

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Hard-core bosons on a triangular lattice with nearest-neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood quantitatively and analytically by constructing quasiparticle excitations of defects that are moving on an ordered background. The location of the solid to supersolid phase transition line is predicted from the effective model for both positive and negative (frustrated) hopping parameters. For positive hopping parameters the calculations agree very accurately with numerical quantum Monte Carlo simulations. The numerical results indicate that the supersolid to superfluid transition is first order.
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We use quantum Monte Carlo method employing stochastic-series-expansion technique to study the ground state properties of the ${t}_{2}\ensuremath{-}{V}_{1}$ model of hard-core bosons on a square lattice. We find that, away from half fillings, the minimal combination of nearest-neighbor repulsion V1{V}_{1}V1​ and next-nearest-neighbor hopping t2{t}_{2}t2​ may give rise to checkerboard supersolidity. The nature of the quantum phase transition, where the superfluid changes to a checkerboard supersolid, depends on the relative strength of V1/t2{V}_{1}/{t}_{2}V1​/t2​ and the average site occupancy. Interestingly, at the half filling, the model displays the extreme Thouless effect. As the filling is varied away from half filling, the model exhibits initially a mixed-order transition, next a tricritical point, and finally a second-order 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 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.
We introduce an inhomogeneous bosonic mixture composed of two kinds of hard-core and semi-hard-core bosons with different nilpotency conditions and demonstrate that in contrast with the standard hard-core Bose-Hubbard model, our bosonic mixture with nearest- and next-nearest-neighbor interactions on a square lattice develops the checkerboard supersolid phase characterized by the simultaneous superfluid and checkerboard solid orders. Our bosonic mixture is created from a two-orbital Bose-Hubbard model including two kinds of bosons: a single-orbital boson and a two-orbital boson. By mapping the bosonic mixture to an anisotropic inhomogeneous spin model in the presence of a magnetic field, we study the ground-state phase diagram of the model by means of cluster mean field theory and linear spin-wave theory and show that various phases such as solid, superfluid, supersolid, and Mott insulator appear in the phase diagram of the mixture. Competition between the interactions and magnetic field causes the mixture to undergo different kinds of first- and second-order phase transitions. By studying the behavior of the spin-wave excitations, we find the reasons of all first- and second-order phase transitions. We also obtain the temperature phase diagram of the system using cluster mean field theory. We show that the checkerboard supersolid phase persists at finite temperature comparable with the interaction energies of bosons.