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arXiv:1311.1604 · Physical Review A

Two-species hard-core bosons on the triangular lattice: A quantum Monte Carlo study

Jian-Ping Lv, Qing‐Hu Chen, Youjin Deng

Published Jan 30, 2014• 18 citations
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Abstract

Using worm-type quantum Monte Carlo simulations, we investigate bosonic mixtures on a triangular lattice of two species of bosons, which interact via nearest-neighbor intraspecies ($V$) and on-site interspecies ($U$) repulsions. For the case of symmetric hopping amplitude (${t}_{A}/V={t}_{B}/V$) and $U/V=1$, we determine a rich ground-state phase diagram that contains double-solid, double-superfluid, supersolid (SS), solid-superfluid (solid-SF), and counterflow supersolid (CSS) states. The SS, solid-SF, and CSS states exhibit spontaneous symmetry breaking among the three sublattices of the triangular lattice and between the two species, which leads to a nonzero crystalline density wave order in each species. We, furthermore, show that the CSS and the SS states are present for ${t}_{A}/V\ensuremath{\ne}{t}_{B}/V$, and the latter even survives up to the ${t}_{A}/V\ensuremath{\rightarrow}\ensuremath{\infty}$ or ${t}_{B}/V\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. The effects induced by the variation of $U/V$ and by the imbalance of particle numbers of the two species are also explored.

DOI
10.1103/physreva.89.013628

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Using worm-type quantum Monte Carlo simulations, we investigate bosonic mixtures on a triangular lattice of two species of bosons, which interact via nearest-neighbor intraspecies (VVV) and on-site interspecies (UUU) repulsions. For the case of symmetric hopping amplitude (tA/V=tB/V{t}_{A}/V={t}_{B}/VtA​/V=tB​/V) and U/V=1U/V=1U/V=1, we determine a rich ground-state phase diagram that contains double-solid, double-superfluid, supersolid (SS), solid-superfluid (solid-SF), and counterflow supersolid (CSS) states. The SS, solid-SF, and CSS states exhibit spontaneous symmetry breaking among the three sublattices of the triangular lattice and between the two species, which leads to a nonzero crystalline density wave order in each species. We, furthermore, show that the CSS and the SS states are present for tA/V\ensuremath≠tB/V{t}_{A}/V\ensuremath{\ne}{t}_{B}/VtA​/V\ensuremath=tB​/V, and the latter even survives up to the tA/V\ensuremath→\ensuremath∞{t}_{A}/V\ensuremath{\rightarrow}\ensuremath{\infty}tA​/V\ensuremath→\ensuremath∞ or tB/V\ensuremath→\ensuremath∞{t}_{B}/V\ensuremath{\rightarrow}\ensuremath{\infty}tB​/V\ensuremath→\ensuremath∞ limit. The effects induced by the variation of U/VU/VU/V and by the imbalance of particle numbers of the two species are also explored.
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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 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.
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