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arXiv:1101.0465 · Physical Review B

Three-body interactions on a triangular lattice

Xue‐Feng Zhang, Yu-Chuan Wen, Yue Yu

Published May 19, 2011• 7 citations
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Abstract

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.

DOI
10.1103/physrevb.83.184513

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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.
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 ${t}_{A}/V\ensuremath{\ne}{t}_{B}/V$, 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/VU/VU/V and by the imbalance of particle numbers of the two species are also explored.
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 systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale quantum Monte Carlo simulations, the ground-state phase diagram is studied. We find a first-order transition between the atomic superfluid phase and the pair superfluid phase when the ratio of the atomic hopping and the atom-pair hopping is adapted. The first-order transition remains unchanged under various conditions. We then focus on the interplay among the atom-pair hopping, the on-site repulsion, and the nearest-neighbor repulsion. With on-site repulsion present, we observe first-order transitions between the Mott insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with 2/32/32/3, 1, and 4/34/34/3 filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasihardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. Without on-site repulsion, the transitions between the pair supersolid and the atom superfluid or pair superfluid are first order, except for the particle-hole symmetric point. With weak on-site repulsion and atom hopping turning on, the transition between the pair supersolid and pair superfluid phase becomes continuous. The transition between solid and pair supersolid is three-dimensional XYXYXY university, with dynamical exponent z=1z=1z=1 and correlation exponent $\ensuremath{\nu}=0.671\phantom{\rule{0.16em}{0ex}}55$. The thermal melting of pair supersolid belongs to the two-dimensional Ising university. We check both energetic and mechanical balance of pair supersolid phase. Lowering the three-body constraint, no pair supersolid is found due to the absence of degeneracy of pair solids in classical limits. We describe the experimental realization of pair tunneling on state dependent lattice.
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 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 extended hard-core Bose-Hubbard model with nearest-neighbor interactions on a triangular lattice with spatial anisotropy by quantum Monte Carlo simulations. The effects of the geometric frustration or the anisotropic strength, represented by the ratio ${t}^{\ensuremath{'}}/t$ between the intrachain nearest-neighbor hopping ${t}^{\ensuremath{'}}$ and the interchain hopping ttt, are studied. We find that for small values of anisotropy ratio ${t}^{\ensuremath{'}}/t$, a solid state emerges at $\ensuremath{\rho}=1/2$ and a supersolid is unstable toward phase separation; for large values of anisotropy ratio ${t}^{\ensuremath{'}}/t$, solid states emerge at $\ensuremath{\rho}=1/3$, 2/3, and a supersolid phase is stable in the region $\ensuremath{\rho}<2/3$; for intermediate values of anisotropy ratio ${t}^{\ensuremath{'}}/t$, three kinds of solid states at fillings $\ensuremath{\rho}=1/3$, 1/2, and $\ensuremath{\rho}=2/3$ coexist and no stable supersolid phase is observed. At half filling, we find that with increasing frustration ${t}^{\ensuremath{'}}/t$, the $\ensuremath{\rho}=1/2$ solid transitions indirectly into the supersolid via an intervening superfluid.