Phase structure of repulsive hard-core bosons in a stacked triangular lattice

Abstract

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...

Bosonict–JModel in a Stacked Triangular Lattice and Its Phase Diagram

“…The original path-integral representation of the partition function contains terms likeā i ∂ τ a i , wherē a i is the complex number corresponding to a † i and τ is the imaginary time. As we discussed in the previous papers 13) and also showed explicitly by the numerical studies on certain models, 4,14,15) effect of non-zero Matsubara-frequency modes in the 3D system at finite temperature is mostly the renormalization of the critical temperature and then the partition function in Eq. (4) is a good approximation for studying phase diagram at finite-T .…”

“…(4) is quite similar to that of the 2D system at T = 0 as verified in the previously studied cases. 4,14,15) In other words, the spatial third direction perpendicular to the 2D lattices plays a role similar to the imaginary-time direction. More detailed discussion on the model (1) at T = 0 will be given in a future publication.…”

“…Relation between the geometrical frustration and the formation of supersolid was discussed previously for the hard-core bosons in a triangular lattice. 3,4) In addition to its own theoretical interest, another motivation for studying the model (1) with the antiferromagnetic (AF) coupling is provided by its relation to the fermionic t-J model. Recently, the fermionic t-J model was studied by mapping it to a kind of bosonic t-J model by using a Chern-Simons gauge field.…”

“…Among them, recent experiments on 4 He under pressure have led to renewed interest of supersolid. 1) Also the search for a lattice supersolid has been motivated by the realization of optical lattices in ultracold atomic systems.…”

“…3,4) This provides example of old idea 5) that a finite density of defects in the solid (vacancies or interstitials) may Bose condense and form a superfluid in the existing crystalline background. In this paper we shall pursue the possibility of realization of "vacancy condensation" phenomenon 6) in boson systems in a triangular lattice in which a frustration exists.…”