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arXiv:cond-mat/9711209 · Physical review. B, Condensed matter

Phase diagrams, critical, and multicritical behavior of hard-core Bose-Hubbard models

Christian Pich, Erwin Frey

Published Jun 1, 1998• 24 citations
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Abstract

We determine the zero-temperature phase diagram of the hard-core Bose-Hubbard model on a square lattice by mean-field theory supplemented by a linear spin-wave analysis. Due to the interplay between nearest- and next-nearest-neighbor interaction and cubic anisotropy several supersolid phases with checkerboard, stripe-domain, or intermediate symmetry are stabilized. The phase diagrams show three different topologies depending on the relative strength of nearest- and next-nearest-neighbor interaction. We also find a rich variety of new quantum critical behavior and multicritical points and discuss the corresponding effective actions and universality classes.

DOI
10.1103/physrevb.57.13712

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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.
We introduce an inhomogeneous bosonic mixture composed of two kinds of hard-core and semi-hard-core bosons with different nilpotency conditions and demonstrate that in contrast with the standard hard-core Bose-Hubbard model, our bosonic mixture with nearest- and next-nearest-neighbor interactions on a square lattice develops the checkerboard supersolid phase characterized by the simultaneous superfluid and checkerboard solid orders. Our bosonic mixture is created from a two-orbital Bose-Hubbard model including two kinds of bosons: a single-orbital boson and a two-orbital boson. By mapping the bosonic mixture to an anisotropic inhomogeneous spin model in the presence of a magnetic field, we study the ground-state phase diagram of the model by means of cluster mean field theory and linear spin-wave theory and show that various phases such as solid, superfluid, supersolid, and Mott insulator appear in the phase diagram of the mixture. Competition between the interactions and magnetic field causes the mixture to undergo different kinds of first- and second-order phase transitions. By studying the behavior of the spin-wave excitations, we find the reasons of all first- and second-order phase transitions. We also obtain the temperature phase diagram of the system using cluster mean field theory. We show that the checkerboard supersolid phase persists at finite temperature comparable with the interaction energies of bosons.
The effect of the next-nearest-neighbor (nnn) tunneling on the hard-core extended Bose–Hubbard model on square lattices is investigated. By means of the cluster mean-field theory, the ground-state phase diagrams are determined. When a modest nnn tunneling is introduced, depending on its sign, two distinct supersolid (SS) states with checkerboard crystal structures are found away from half-filing. The characters of various phase transitions out of these two SS states are discussed. In particular, for the case with kinetic frustration, the existence of a half SS phase possessing both solid and unconventional superfluid orders is established. Our work hence sheds light on the search of this interesting SS phase in real ultracold lattice gases with frustrated tunnelings.
We investigate the Bose-Einstein condensation (BEC) patterns, the critical and multicritical behaviors of three-dimensional mixtures of bosonic gases with density-density interactions, characterized by a global $\mathrm{U}(1)\ensuremath{\bigoplus}\mathrm{U}(1)$ symmetry [one U(1) transformation for each species]. In particular, we consider the three-dimensional Bose-Hubbard model for two lattice bosonic gases coupled by an on-site interspecies density-density interaction. We study the phase diagram and the critical behaviors along the transition lines of the BEC of one or both species. We present mean-field calculations and finite-size scaling analyses of quantum Monte Carlo data. We also investigate the nature of the multicritical points where the BEC transition lines of the two species meet. The corresponding universality classes are inferred from a renormalization-group analysis of the corresponding multicritical $\mathrm{U}(1)\ensuremath{\bigoplus}\mathrm{U}(1)$ Landau-Ginzburg-Wilson ${\mathrm{\ensuremath{\Phi}}}^{4}$ theory. We find two distinct critical behaviors, associated with bicritical and tetracritical points, respectively, depending on the relative strength of the interspecies and intraspecies interactions.
By using the inhomogeneous mean-field theory, the phase diagram of the two-dimensional soft-core extended Bose-Hubbard model with both on-site and nearest-neighbor interactions in the presence of spatial disorder is determined. Rich phases, including Mott-insulator, checkerboard solid, supersolid, superfluid and disordered solid are obtained. Interestingly, due to the presence of disorder, a new disordered solid phase is found between the incompressible lobes, and it is demonstrated that the supersolid phase can survive in two-dimensional soft-core bosons. Furthermore, the system undergoes the phase transition from a disordered solid into a solid order or supersolid landscape when the disorder strength is increased. For weak nearest-neighbor repulsion, the increase of the disorder strength induces both checkerboard solid and supersolid phases shrinking to smaller hopping regions. However, for strong nearest-neighbor repulsion, the disorder stabilizes the supersolid phase and makes it occupying a remarkably broad region in the phase diagram. The analytical expressions for the phase boundaries between the incompressible and compressible phases are also obtained, which are in qualitative agreement with our numerical results.
We analyze the hard-core Bose-Hubbard model with both three-body and nearest-neighbor repulsions on a triangular lattice. The phase diagram is achieved by means of the semiclassical approximation and a quantum Monte Carlo simulation. For a system with only three-body interactions, both the supersolid phase and the one-third solid disappear while the two-thirds solid is stable. As the thermal behavior of the bosons with nearest-neighbor repulsion, the solid and the superfluid undergo the three-state Potts- and Kosterlitz--Thouless-type phase transitions, respectively. In a system with both frustrated nearest-neighbor two-body and three-body interactions, the supersolid and one-third solid are revived. By tuning the strength of the three-body interactions, the phase diagram is distorted because the one-third solid and the supersolid are suppressed.