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AIP conference proceedings

Supersolid Bosons on the Triangular Lattice

Stefan Weßel

Published Jan 1, 2006• 0 citations
Publisher

Abstract

The zero temperature phase diagram of hardcore bosons on the triangular lattice with nearest neighbor repulsion is determined using quantum Monte Carlo simulations. The system exhibits an extended supersolid phase emerging from an order‐by‐disorder effect as a novel way of a quantum system to avoid classical frustration. We analyze the nature of the supersolid phase and its stability in competition with phase‐separation, which we find to occurs in other regions of parameter space.

DOI
10.1063/1.2178049

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The zero temperature phase diagram of hardcore bosons on the triangular lattice with nearest neighbor repulsion is determined using quantum Monte Carlo simulations. The system exhibits an extended supersolid phase emerging from an order‐by‐disorder effect as a novel way of a quantum system to avoid classical frustration. We analyze the nature of the supersolid phase and its stability in competition with phase‐separation, which we find to occurs in other regions of parameter space.
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.
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.
We analyze the hard-core Bose-Hubbard model with both three-body and nearest-neighbor repulsions on a triangular lattice. The phase diagram is achieved by means of the semiclassical approximation and a quantum Monte Carlo simulation. For a system with only three-body interactions, both the supersolid phase and the one-third solid disappear while the two-thirds solid is stable. As the thermal behavior of the bosons with nearest-neighbor repulsion, the solid and the superfluid undergo the three-state Potts- and Kosterlitz--Thouless-type phase transitions, respectively. In a system with both frustrated nearest-neighbor two-body and three-body interactions, the supersolid and one-third solid are revived. By tuning the strength of the three-body interactions, the phase diagram is distorted because the one-third solid and the supersolid are suppressed.
In this Brief Report, we study phase structure of a system of hard-core bosons with a nearest-neighbor (NN) repulsive interaction in a stacked triangular lattice. The Hamiltonian of the system contains two parameters, one of which is the hopping amplitude ttt between NN sites and the other is the NN repulsion VVV. We investigate the system by means of the Monte Carlo simulations and clarify the low- and high-temperature phase diagrams. Phase diagrams contain various phases, e.g., solid, superfluid, supersolid, and phase-separated states. The result is compared with the phase diagram of the two-dimensional system in a triangular lattice at vanishing temperature.
We numerically demonstrate that a supersolid phase exists in a frustrated hard-core boson system on a triangular lattice over a wide range of interaction strength. In the infinite repulsion (Ising) limit, we establish a mapping to the same problem with unfrustrated hopping, which connects the supersolid to the known results in that case. The weak superfluidity can be destroyed or strongly enhanced by a next-nearest-neighbor hopping term, which provides valuable information for experimental realization of a supersolid phase on optical lattice. A phase diagram for the frustrated anisotropic Heisenberg model on triangular lattice is also established.