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arXiv:cond-mat/0507620 · Physical Review Letters

Supersolid Phase of Hard-Core Bosons on a Triangular Lattice

Massimo Boninsegni, Nikolay V. Prokof'ev

Published Nov 28, 2005• 199 citations
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Abstract

We study properties of the supersolid phase observed for hard-core bosons on the triangular lattice near half-integer filling factor, and the phase diagram of the system at finite temperature. We find that the solid order is always of the (2m, -m, -m) with m changing discontinuously from positive to negative values at half filling, in contrast with phases observed for Ising spins in a transverse magnetic field. At finite temperature we find two intersecting second-order transition lines: one in the 3-state Potts universality class and the other of the Kosterlitz-Thouless type.

DOI
10.1103/physrevlett.95.237204

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We study properties of the supersolid phase observed for hard-core bosons on the triangular lattice near half-integer filling factor, and the phase diagram of the system at finite temperature. We find that the solid order is always of the (2m, -m, -m) with m changing discontinuously from positive to negative values at half filling, in contrast with phases observed for Ising spins in a transverse magnetic field. At finite temperature we find two intersecting second-order transition lines: one in the 3-state Potts universality class and the other of the Kosterlitz-Thouless type.
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 the extended hard-core Bose–Hubbard model in a two-dimensional anisotropic triangular lattice by quantum Monte Carlo simulations. We present the ground state phase diagram at half filling. Four kinds of phases, including two solid phases, a superfluid phase and a supersolid phase, are observed. The supersolid phase exists only in a narrow region close to the isotropic limit. Away from half filling, we find that the results are strongly dependent on the phase at half filling. No supersolid phase exists if the ground state at half filling is a superfluid or a solid.
We study ground state properties and excitation spectra for hard-core bosons on square and triangular lattices, at half filling, using series expansion methods. Nearest-neighbor repulsion between the bosons leads to the development of short-range density order at the antiferromagnetic wave vector, and simultaneously, a minimum in the density excitation spectra. On the square lattice, the model maps onto the well studied XXZXXZXXZ model, and the gap at the minimum collapses to zero precisely at the Heisenberg symmetry point, leading to the well known spectra for the Heisenberg antiferromagnet. On the triangular lattice, the collapse of the gap at the minimum signals the onset of the supersolid phase. Our results suggest that the transition from the superfluid to the supersolid phase may be weakly first order. We also find several features in the density of states, including two peaks and a sharp discontinuity, which may be observable in experimental realization of such systems.
We study ground state properties and excitation spectra for hard-core Bosons on square and triangular lattices, at half filling, using series expansion methods. Nearest-neighbor repulsion between the Bosons leads to the development of short-range density order at the antiferromagnetic wavevector, and simultaneously a roton minima in the density excitation spectra. On the square-lattice, the model maps on to the well studied XXZ model, and the roton gap collapses to zero precisely at the Heisenberg symmetry point, leading to the well known spectra for the Heisenberg antiferromagnet. On the triangular-lattice, the collapse of the roton gap signals the onset of the supersolid phase. Our results suggest that the transition from the superfluid to the supersolid phase maybe weakly first order. We also find several features in the density of states, including two-peaks and a sharp discontinuity, which maybe observable in experimental realization of such systems.
We study the properties of $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}V$ model of hard-core bosons on the triangular lattice that can be realized in optical lattices. By mapping to the spin-1∕21∕21∕2 XXZXXZXXZ model in a field, we determine the phase diagram of the $t\text{\ensuremath{-}}V$ model where the supersolid characterized by the ordering pattern $(x,x,\ensuremath{-}2{x}^{\ensuremath{'}})$ (``ferrimagnetic'' or SS AAA) is a ground state for chemical potential $\ensuremath{\mu}>3V$. By turning on either temperature or ${t}^{\ensuremath{'}}$ at half filling $(\ensuremath{\mu}=3V)$, we find a first order transition from SS AAA to the elusive supersolid characterized by the $(x,\ensuremath{-}x,0)$ ordering pattern (``antiferromagnetic'' or SS CCC). In addition, we find a large region where a superfluid phase becomes a solid upon increasing temperature at fixed chemical potential. This is an analog of the Pomeranchuk effect driven by the large entropic effects associated with geometric frustration on the triangular lattice.
We study the soft-core extended Bose-Hubbard model in a two-dimensional triangular lattice by using the quantum Monte Carlo methods. The ground-state phase diagram of the system exhibits a very fruitful structure and is much intriguing. Aside from the Mott insulating state, four kinds of solid states with respect to the commensurate filling factors $\ensuremath{\rho}=1∕3,2∕3$ and $\ensuremath{\rho}=1$ are identified. In incommensurate fillings, superfluid, supersolid, as well as phase-separation states are detected. As in the case of the hard-core bosons, a supersolid phase exists in $1∕3<\ensuremath{\rho}<2∕3$ while it is unstable toward the phase separation in $\ensuremath{\rho}<1∕3$. However, this instability is refrained in $2∕3<\ensuremath{\rho}<1$ due to the softening of the bosons, and then a supersolid phase survives.