In this paper, we consider the bosonic t-J model, which describes two-component hard-core bosons with a nearest-neighbor (NN) pseudo-spin interaction and a NN hopping. To study 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 our 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 easyplane pseudo-spin. Coherent condensates of the phases describe, e.g., a "magnetic order" of the pseudo-spin, 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 MonteCarlo 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 pseudo-spin degrees of freedom and boson fields of the original two-component hardcore bosons. As 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.

In this paper, we study quantum Sp(N) antiferromagnetic (AF) Heisenberg models in two dimensions (2D) by using the Schwinger-boson representation and the pathintegral methods. An effective field theory, which is an extension of CP N −1 model in (2+1)D, is derived and its phase structure is studied by the 1/N -expansion. We introduce a spatial anisotropy in the exchange couplings and show that the effective coupling constant in the CP N −1 model is an increasing function of the anisotropy.For the SU(N) AF Heisenberg model, which is a specific case of the Sp(N) model, we found that phase transition from the ordered "Néel state" to paramagnetic phase takes place as the anisotropy is increased. In the vicinity of the SU(N) symmetric point, this phase structure is retained. However as a parameter that controls explicit breaking of the SU(N) symmetry is increased, a new phase, which is similar to the spiral-spin phase with a nematic order in frustrated SU(2) spin systems, appears.It is shown that at that phase transition point, a local SU(2) gauge symmetry with composite SU(2) gauge field appears in the low-energy sector. It is another example of symmetry-enhancement phenomenon at low energies. We also introduce a lattice gauge-theoretical model, which is a counterpart of the effective field theory, and study its phase structure by means of the Monte-Carlo simulations.

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. Physical states of the system are restricted to the ones without the doubly-occupied state at each site. 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 pseudo-spin pattern with the 120 o structure.