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arXiv:1210.7910 · Physical Review B

Effective field theories for two-component repulsive bosons on lattice and their phase diagrams

Yoshihito Kuno, Keisuke Kataoka, Ikuo Ichinose

Published Jan 31, 2013• 10 citations
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Abstract

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.

DOI
10.1103/physrevb.87.014518

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In this paper, we study phase diagrams of dipolar hard-core boson gases on a honeycomb lattice. The system is described by the Haldane-Bose-Hubbard model with complex hopping amplitudes and nearest-neighbor repulsion. By using the slave-particle representation of the hard-core bosons and also the path-integral quantum Monte Carlo simulations, we investigate the system and show that the systems have a rich phase diagram. There are Mott, superfluid, chiral superfluid, and sublattice chiral superfluid phases as well as the density-wave phase. We also found a coexisting phase of superfluid and chiral superfluid. Critical behaviors of the phase transitions are also clarified.