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arXiv:0707.0866 · Physical Review B

Supersolidity, entropy, and frustration: t−t′−V model of hard-core bosons on the triangular lattice

Syed R. Hassan, Luca de’ Medici, A.–M. S. Tremblay

Published Oct 16, 2007• 37 citations
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Abstract

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-$1∕2$ $XXZ$ 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 $A$) 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 $A$ to the elusive supersolid characterized by the $(x,\ensuremath{-}x,0)$ ordering pattern (``antiferromagnetic'' or SS $C$). 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.

DOI
10.1103/physrevb.76.144420

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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.
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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 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.
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.