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Physical Review B

Finite-temperature phase diagram of the three-dimensional hard-core bosonic t - J model

Yuki Nakano, Takumi Ishima, Naohiro Kobayashi, Kazuhiko Sakakibara, Ikuo Ichinose, Tetsuo Matsui

Published Jun 8, 2011• 14 citations
Publisher

Abstract

We study the three-dimensional bosonic $t$-$J$ model, that is, the $t$-$J$ 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 $x$ with a two-component spin $\ensuremath{\sigma}(=$$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 (CP${}^{1}$ 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 $t$-$J$ 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 $t$-$J$ model has a phase diagram that suggests some interesting implications for high-temperature superconducting materials.

DOI
10.1103/physrevb.83.235116

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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 Bx\ensuremathσ{B}_{x\ensuremath{\sigma}}Bx\ensuremathσ​ at the site xxx with a two-component spin \ensuremath{\sigma}(=$$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) zx\ensuremathσ{z}_{x\ensuremath{\sigma}}zx\ensuremathσ​ and a holon described by a hard-core-boson field \ensuremathϕx{\ensuremath{\phi}}_{x}\ensuremathϕx​ as Bx\ensuremathσ=\ensuremathϕx\ifmmode†\else\textdagger\fizx\ensuremathσ{B}_{x\ensuremath{\sigma}}={\ensuremath{\phi}}_{x}^{\ifmmode\dagger\else\textdagger\fi{}}{z}_{x\ensuremath{\sigma}}Bx\ensuremathσ​=\ensuremathϕx\ifmmode†\else\textdagger\fi​zx\ensuremathσ​. 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 t-J model, i.e., the t-J model of "bosonic electrons" at finite temperatures. This model describes a system of cold bosonic atoms with two species in an optical lattice. The model is derived from the Hubbard model for very large on-site repulsive interaction between bosons of same species (hard-core nature) and also strong correlations between different species. The operator B_{xσ} for an atom at the site x with a two-component (pseudo-) spin σ(=1,2) is treated as a hard-core boson operator, and represented by a composite of two slave particles; a spinon described by a CP^1 field (Schwinger boson) z_{xσ} and a holon described by a hard-core-boson field ϕ_x as B_{xσ}=ϕ^†_x z_{xσ}. ϕ_x is then expressed by a pseudo-spin, which is, in turn, represented by another CP^1 (pseudo) spinon w_{xη} as ϕ_x = w_{x2}^†w_{x1}. We then have a double-CP^1 representation of the model by z_{xσ} and w_{xη}. By means of Monte Carlo simulations of this bosonic t-J model, we study its phase structure and the possible phenomena like appearance of antiferromagnetic long-range order, Bose-Einstein condensation, phase separation, etc. They should be compared with the possible experimental results of a recently studied boson-boson mixture like ^87Rb and ^41K in an optical lattice.
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.
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We study the three-dimensional U(1) lattice gauge theory of a CP1^11 spinon (Schwinger boson) field and a Higgs field. It is a bosonic ttt-JJJ model in slave-particle representation, describing the antiferromagnetic (AF) Heisenberg spin model with doped bosonic holes expressed by the Higgs field. The spinon coupling term of the action favors AF long-range order, whereas the holon hopping term in the ferromagnetic channel favors Bose-Einstein condensation (BEC) of holons. We investigate the phase structure by means of Monte-Carlo simulations and study an interplay of AF order and BEC of holes. We consider the two variations of the model; (i) the three-dimensional model at finite temperatures, and (ii) the two-dimensional model at vanishing temperature. In the model (i) we find that the AF order and BEC coexist at low temperatures and certain hole concentrations. In the model (ii), by varying the hole concentration and the stiffness of AF spin coupling, we find a phase diagram similar to the model (i). Implications of the results to systems of cold atoms and the fermionic ttt-JJJ model of strongly-correlated electrons are discussed.
We study the system of hard-core bosons (HCB) with two species in the three-dimensional lattice at finite temperatures. In the strong-correlation limit, the system becomes the t-J model, that is, the t-J model of bosonic electrons. The electron operator Bxσ at the site x with a two-component spin σ(= 1, 2***) is treated as a HCB operator, and represented by a composite of two slave particles; a spinon described by a Schwinger boson (CP1 boson) zxσ and a holon described by a HCB field x as Bxσ = †xzxσ.*** This x is again represented by another CP1 quasi-spinon operator ωxa*** (a = 1, 2***). The phase diagrams of the resulting double CP1 system obtained by Monte Carlo simulations involve first-order and second-order phase boundaries. We present in detail the techniques and algorithm to reduce the hysteresis and locate the first-order transition points.
In the present paper, we study finite-temperature phase structure of two-component hard-core bosons in a cubic optical lattice. The system that we study in the present paper is an effective model for the Bose-Hubbard model with strong on-site repulsions and is called bosonic t-J model. This model is a bosonic counterpart of the t-J model for the strongly-correlated electron systems like the high-temperature superconducting materials. We study the model by means of path-integral methods and Monte-Carlo simulations. We found that this system has a very rich phase structure including checkerboard-type "insulating" state, superfluid, phase-separated state, inhomogeneous cloudlet state, etc. We are also interested in the possible supersolid phase with both the checkerboard order and superfluidity and found that additional nearest-neighbor inter-species attractive force induces the supersolid state. In the supersolid state, paired superfluid appears in addition to the superfluid of single atom. This result gives important insight into mechanism of the high-temperature superconductivity of the cuprate.
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.