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Physical Review B

Mixed columnar-plaquette phase of hard-core bosons and its quantum melting

Stefan Weßel

Published Aug 18, 2008• 7 citations
Publisher

Abstract

We examine the ground-state phase diagram of repulsively interacting hard-core bosons on the quarter-filled checkerboard lattice using quantum Monte Carlo simulations constrained to the canonical ensemble. At a sufficiently large repulsion, the system undergoes a quantum phase transition from a superfluid into a valence-bond-solid regime. We identify this as a weakly first-order quantum melting transition at quarter filling. Furthermore, by examining appropriate order parameters, we exhibit the mixed nature of the valence bond solid, with both columnar and plaquette long-ranged order. Our results demonstrate the realization of the mixed columnar-plaquette phase found recently for the square lattice quantum dimer model in a microscopic bosonic system.

DOI
10.1103/physrevb.78.075112

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We examine the ground-state phase diagram of repulsively interacting hard-core bosons on the quarter-filled checkerboard lattice using quantum Monte Carlo simulations constrained to the canonical ensemble. At a sufficiently large repulsion, the system undergoes a quantum phase transition from a superfluid into a valence-bond-solid regime. We identify this as a weakly first-order quantum melting transition at quarter filling. Furthermore, by examining appropriate order parameters, we exhibit the mixed nature of the valence bond solid, with both columnar and plaquette long-ranged order. Our results demonstrate the realization of the mixed columnar-plaquette phase found recently for the square lattice quantum dimer model in a microscopic bosonic system.
Using large scale quantum Monte Carlo simulations and dual vortex theory, we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest-neighbor repulsion. In contrast with the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half filling, two novel solid phases emerge at densities rho=1/3 and rho=2/3. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid.
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.
Using large scale quantum Monte Carlo simulations and dual vortex theory we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest neighbor repulsion. In contrast to the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half-filling, two novel solid phases emerge at densities ρ=1/3\rho=1/3ρ=1/3 and ρ=2/3\rho=2/3ρ=2/3. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid.
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 hard-core bosons on the checkerboard lattice with nearest-neighbor unfrustrated hopping ttt and ``tetrahedral'' plaquette charging energy UUU. Analytical arguments and quantum Monte Carlo simulations lead us to the conclusion that the system undergoes a zero temperature (T)(T)(T) quantum phase transition from a superfluid phase at small U∕tU∕tU∕t to a large U∕tU∕tU∕t Mott insulator phase with $\ensuremath{\rho}=1∕4$ for a range of values of the chemical potential $\ensuremath{\mu}$. Further, the quarter-filled insulator breaks lattice translation symmetry in a characteristic fourfold ordering pattern and occupies a lobe of finite extent in the $\ensuremath{\mu}\text{\ensuremath{-}}U∕t$ phase diagram. A quantum Monte Carlo study slightly away from the tip of the lobe provides evidence for a direct weakly first-order superfluid insulator transition away from the tip of the lobe. While analytical arguments lead us to conclude that the transition at the tip of the lobe belongs to a different Landau-forbidden second-order universality class, an extrapolation of our numerical results suggests that the size of the first-order jump does not go to zero even at the tip of the lobe.
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.