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arXiv:1111.1537 · Physical Review A

Finite-temperature phase diagram of two-component bosons in a cubic optical lattice: Three-dimensional t - J model of hard-core bosons

Yuki Nakano, Takumi Ishima, Naohiro Kobayashi, Takahiro S. Yamamoto, Ikuo Ichinose, Tetsuo Matsui

Published Feb 13, 2012• 16 citations
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Abstract

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 $s=\frac{1}{2}$ 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.

DOI
10.1103/physreva.85.023617

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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 $s=\frac{1}{2}$ 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 Br\ensuremathσ{B}_{r\ensuremath{\sigma}}Br\ensuremathσ​ at the site rrr with a two-component (pseudo)spin \ensuremathσ(=1,2)\ensuremath{\sigma}(=1,2)\ensuremathσ(=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 \ensuremathα\ensuremath{\alpha}\ensuremathα 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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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.
The bosonic t-J model is a strong-on-site repulsion limit of the two-component Bose-Hubbard model and is expected to be realized by experiments of cold atoms in an optical lattice. In previous papers, we studied the bosonic t-J model by both analytical methods and numerical Monte - Carlo (MC) simulations. However, in the case of finite JzJ_zJz​, where JzJ_zJz​ is the zzz-component coupling constant of the pseudospin interaction, the phase diagram of the model was investigated by assuming the checkerboard type of boson densities. In this study, we shall continue our previous study of the bosonic t-J model using both the Gross-Pitaevskii (GP) theory and MC simulations without assuming any pattern of boson densities. These two methods complement each other and give reliable results. We show that as JzJ_zJz​ is increased, the superfluid state evolves into a supersolid (SS), and furthermore into a genuine solid with the checkerboard symmetry. In the present study, we propose a method identifying quantum phase transitions in the GP theory. We also study finite-temperature phase transitions of the superfluidity and the diagonal solid order of the SS by MC simulations.
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 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.