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arXiv:1206.5358 · Journal of the Physical Society of Japan

Bosonict–JModel in a Stacked Triangular Lattice and Its Phase Diagram

Keisuke Kataoka, Yoshihito Kuno, Ikuo Ichinose

Published Nov 19, 2012• 5 citations
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Abstract

In this paper, we study phase diagram of a system of two-component hard-core bosons with nearest-neighbor (NN) pseudo-spin antiferromagnetic (AF) interactions in a stacked triangular lattice. Hamiltonian of the system contains three parameters one of which is the hopping amplitude $t$ between NN sites, and the other two are the NN pseudo-spin exchange interaction $J$ and the one that measures anisotropy of pseudo-spin interactions. We investigate the system by means of the Monte-Carlo simulations and clarify the low-temperature phase diagram. In particular, we are interested in how the competing orders, i.e., AF order and superfluidity, are realized, and also whether supersolid forms as a result of hole doping into the state of the $\sqrt{3}\times \sqrt{3}$ pseudo-spin pattern with the $120^o$ structure.

DOI
10.1143/jpsj.81.124502

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In this paper, we study phase diagram of a system of two-component hard-core bosons with nearest-neighbor (NN) pseudo-spin antiferromagnetic (AF) interactions in a stacked triangular lattice. Hamiltonian of the system contains three parameters one of which is the hopping amplitude ttt between NN sites, and the other two are the NN pseudo-spin exchange interaction JJJ and the one that measures anisotropy of pseudo-spin interactions. We investigate the system by means of the Monte-Carlo simulations and clarify the low-temperature phase diagram. In particular, we are interested in how the competing orders, i.e., AF order and superfluidity, are realized, and also whether supersolid forms as a result of hole doping into the state of the 3×3\sqrt{3}\times \sqrt{3}3​×3​ pseudo-spin pattern with the 120o120^o120o structure.
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.
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 paper, we consider the bosonic ttt-JJJ model, which describes two-component hard-core bosons with a nearest-neighbor (NN) pseudospin interaction and a NN hopping. To study the phase diagram of this model, we derive effective field theories for low-energy excitations. In order to represent the hard-core nature of bosons, we employ a slave-particle representation. In the path-integral quantization, we first integrate out the radial degrees of freedom of each boson field and obtain the low-energy effective field theory of phase degrees of freedom of each boson field and an easy-plane pseudospin. Coherent condensates of the phases describe, e.g., a ``magnetic order'' of the pseudospin, superfluidity of hard-core bosons, etc. This effective field theory is a kind of extended quantum XYXYXY model, and its phase diagram can be investigated precisely by means of the Monte Carlo simulations. We then apply a kind of Hubbard-Stratonovich transformation to the quantum XYXYXY model and obtain the second version of the effective field theory, which is composed of fields describing the pseudospin degrees of freedom and boson fields of the original two-component hard-core bosons. As an application of the effective-field theory approach, we consider the bosonic ttt-JJJ model on the square lattice and also on the triangular lattice, and compare the obtained phase diagrams with the results of the numerical studies. We also study low-energy excitations rather in detail in the effective field theory. Finally, we consider the bosonic ttt-JJJ model on a stacked triangular lattice and obtain its phase diagram. We compare the obtained phase diagram with that of the effective field theory to find close resemblance.
We study the three-dimensional bosonic ttt-JJJ model, i.e., the ttt-JJJ model of ``bosonic electrons,'' at finite temperatures. This model describes the s=12s=\frac{1}{2}s=21​ Heisenberg spin model with the anisotropic exchange coupling ${J}_{\ensuremath{\perp}}=\ensuremath{\alpha}{J}_{z}$ and doped bosonic holes, which is an effective system of the Bose-Hubbard model with strong repulsions. The bosonic ``electron'' operator ${B}_{r\ensuremath{\sigma}}$ at the site rrr with a two-component (pseudo)spin $\ensuremath{\sigma}(=1,2)$ is treated as a hard-core boson operator. By means of Monte Carlo simulations, we study its finite-temperature phase structure including the $\ensuremath{\alpha}$ dependence, the possible phenomena-like appearance of checkerboard long-range order, supercounterflow, superfluidity, phase separation, etc. The obtained results, which clarify the relation between various phases, may be taken as predictions about experiments of two-component cold bosonic atoms in a cubic optical lattice.
We study the three-dimensional bosonic ttt-JJJ model, that is, the ttt-JJJ model of ``bosonic electrons'' at finite temperatures. This model describes a system of an isotropic antiferromagnet with doped bosonic holes and is closely related to systems of two-component bosons in an optical lattice. The bosonic ``electron'' operator ${B}_{x\ensuremath{\sigma}}$ at the site xxx with a two-component spin $\ensuremath{\sigma}(=$1,2)1,2)1,2) is treated as a hard-core boson operator and represented by a composite of two slave particles: a spinon described by a Schwinger boson (CP1{}^{1}1 boson) ${z}_{x\ensuremath{\sigma}}$ and a holon described by a hard-core-boson field ${\ensuremath{\phi}}_{x}$ as ${B}_{x\ensuremath{\sigma}}={\ensuremath{\phi}}_{x}^{\ifmmode\dagger\else\textdagger\fi{}}{z}_{x\ensuremath{\sigma}}$. By means of Monte Carlo simulations of this bosonic ttt-JJJ model, we study its phase structure and the possible phenomena like appearance of antiferromagnetic long-range order, Bose-Einstein condensation, phase separation, etc. Obtained results show that the bosonic ttt-JJJ model has a phase diagram that suggests some interesting implications for high-temperature superconducting materials.
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.