In this paper, we study phase structure of a system of hard-core bosons with a nearest-neighbor (NN) repulsive interaction in a stacked triangular lattice. Hamiltonian of the system contains two parameters one of which is the hopping amplitude t between NN sites and the other is the NN repulsion V . We investigate the system by means of the Monte-Carlo simulations and clarify the low and high-temperature phase diagrams. There exist solid states with density of boson ρ = 1 3 and 2 3 , superfluid, supersolid and phase-separated state. The result is compared with the phase diagram of the two-dimensional system in a triangular lattice at vanishing temperature.PACS numbers: 67.85. Hj, 03.75.Nt In recent years, cold-atomic systems are one of the most intensively studied topics not only in atomic physics but also in condensed matter physics. In particular, study on cold-atom systems put on an optical lattice may give very important insight about dynamics of stronglycorrelated particle systems 1 . For systems in an optical lattice, interactions between atoms, dimensionality of system, etc. are highly controllable, and effects of impurities are strongly suppressed. Among many interesting topics, possibility of the appearance of the supersolid (SS) has been investigated intensively. In the SS, the superfluidity and a diagonal long-range order (DLRO) such as density wave coexist. It has been clarified that the SS cannot exist in a hard-core (HC) boson system in a square lattice unless long-range interactions between bosons are included 2 . On the other hand on a triangular lattice, it was shown that the SS can appear as a result of the competition between the particle hopping and nearest-neighbor (NN) repulsion 3,4 .In this paper, we shall pursue the above problem, i.e., we shall consider a three-dimensional (3D) hard-core (HC) boson system in a stacked triangular lattice and study a finite-temperature (T ) phase diagram. As we consider the 3D system, there exist finite-temperature (T ) phase transitions in addition to "quantum phase transition". Hamiltonian of the system is then given bywhere i and j denote site of 3D stacked triangular lattice, φ i is annihilation operator of the HC boson, n i is the number operator n i = φ † i φ i and µ is the chemical potential for the grand-canonical ensemble. i, j denotes the NN sites in the 3D stacked triangular lattice, whereas i, j those of the 2D triangular lattice. t is the hopping amplitude in the 3D lattice, whereas V (> 0) denotes the NN repulsion in the 2D triangular lattice. The HC boson operators φ i satisfy the following (anti)commutation relations,The above HC boson can be expressed in terms of the Schwinger boson w iσ (σ = 1, 2),where the physical-state condition of the Schwinger is given as, σ=1,2where |Phys w is the physical Hilbert space of w iσ . Partition function of the system at temperature (T ) Z = Tr exp(−βH) with β = 1/k B T , is given as follows,whereIn the present study, we shall ignore the τ -dependence of w iσ , and then focus on the finite-T physical p...

We study the interplay of the ferromagnetic (FM) state and the p-wave superconducting (SC) state observed in several materials such as UCoGe and URhGe in a totally nonperturbative manner. To this end, we introduce a lattice Ginzburg-Landau model that is a genuine generalization of the phenomenological Ginzburg-Landau theory proposed previously in the continuum and also a counterpart of the lattice gauge-Higgs model for the s-wave SC transition, and study it numerically by Monte-Carlo simulations. The obtained phase diagram has qualitatively the same structure as that of UCoGe in the region where the two transition temperatrures satisfy TFM > TSC. For TFM/TSC < 0.7, we find that the coexisting region of FM and SC orders appears only near the surface of the lattice, which describes an inhomogeneous FMSC coexisting state.

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