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arXiv:0712.1518 · Physical Review B

Phase diagram of an anisotropic bosonic t−J model

Massimo Boninsegni, Nikolay V. Prokof'ev

Published Mar 5, 2008• 22 citations
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Abstract

We have studied by quantum Monte Carlo simulations the low temperature phase diagram of a mixture of isotopic, hard core bosons, described by the $t\text{\ensuremath{-}}{J}_{z}\text{\ensuremath{-}}{J}_{\ensuremath{\perp}}$ model, with ${J}_{\ensuremath{\perp}}=\ensuremath{\alpha}{J}_{z}$. The coexistence of superfluid hole-rich and insulating, antiferromagnetically ordered hole-free phases is observed at sufficiently low hole density for any $\ensuremath{\alpha}<1$. A two-component checkerboard supersolid phase is not observed. The experimental relevance and possible broader implications of these findings are discussed.

DOI
10.1103/physrevb.77.092502

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We have studied by quantum Monte Carlo simulations the low temperature phase diagram of a mixture of isotopic, hard core bosons, described by the t\ensuremath-Jz\ensuremath-J\ensuremath⊥t\text{\ensuremath{-}}{J}_{z}\text{\ensuremath{-}}{J}_{\ensuremath{\perp}}t\ensuremath-Jz​\ensuremath-J\ensuremath⊥​ model, with J\ensuremath⊥=\ensuremathαJz{J}_{\ensuremath{\perp}}=\ensuremath{\alpha}{J}_{z}J\ensuremath⊥​=\ensuremathαJz​. The coexistence of superfluid hole-rich and insulating, antiferromagnetically ordered hole-free phases is observed at sufficiently low hole density for any \ensuremathα<1\ensuremath{\alpha}<1\ensuremathα<1. A two-component checkerboard supersolid phase is not observed. The experimental relevance and possible broader implications of these findings are discussed.
We introduce an inhomogeneous bosonic mixture composed of two kinds of hard-core and semi-hard-core bosons with different nilpotency conditions and demonstrate that in contrast with the standard hard-core Bose-Hubbard model, our bosonic mixture with nearest- and next-nearest-neighbor interactions on a square lattice develops the checkerboard supersolid phase characterized by the simultaneous superfluid and checkerboard solid orders. Our bosonic mixture is created from a two-orbital Bose-Hubbard model including two kinds of bosons: a single-orbital boson and a two-orbital boson. By mapping the bosonic mixture to an anisotropic inhomogeneous spin model in the presence of a magnetic field, we study the ground-state phase diagram of the model by means of cluster mean field theory and linear spin-wave theory and show that various phases such as solid, superfluid, supersolid, and Mott insulator appear in the phase diagram of the mixture. Competition between the interactions and magnetic field causes the mixture to undergo different kinds of first- and second-order phase transitions. By studying the behavior of the spin-wave excitations, we find the reasons of all first- and second-order phase transitions. We also obtain the temperature phase diagram of the system using cluster mean field theory. We show that the checkerboard supersolid phase persists at finite temperature comparable with the interaction energies of bosons.
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.
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 determine the finite-temperature phase diagram of the square lattice hard-core boson Hubbard model with nearest neighbor repulsion using quantum Monte Carlo simulations. This model is equivalent to an anisotropic spin-1/2 XXZ model in a magnetic field. We present the rich phase diagram with a first order transition between a solid and superfluid phase, instead of a previously conjectured supersolid and a tricritical end point to phase separation. Unusual reentrant behavior with ordering upon increasing the temperature is found, similar to the Pomeranchuk effect in 3He.
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.
We study the ground state properties of the extended hard-core Bose–Hubbard model in a two-dimensional anisotropic triangular lattice by quantum Monte Carlo simulations. We present the ground state phase diagram at half filling. Four kinds of phases, including two solid phases, a superfluid phase and a supersolid phase, are observed. The supersolid phase exists only in a narrow region close to the isotropic limit. Away from half filling, we find that the results are strongly dependent on the phase at half filling. No supersolid phase exists if the ground state at half filling is a superfluid or a solid.