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.
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
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.
We study the three-dimensional bosonic
t-
J model, i.e., the
t-
J model of ``bosonic electrons,'' at finite temperatures. This model describes the
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
r 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 U(1) lattice gauge theory of a CP
1 spinon (Schwinger boson) field and a Higgs field. It is a bosonic
t-
J 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
t-
J model of strongly-correlated electrons are discussed.
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 consider the bosonic
t-
J 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
XY 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
XY 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
t-
J 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
t-
J 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.