Bose-Hubbard model on a star lattice

We analyze the Bose-Hubbard model of hardcore bosons with nearest neighbor hopping and repulsive interactions on a star lattice using both quantum Monte Carlo simulation and dual vortex theory. We obtain the phase diagram of this model as a function of the chemical potential and the relative strength of hopping and interaction. In the strong interaction regime, we find that the Mott phases of the model at 1/2 and 1/3 fillings, in contrast to their counterparts on square, triangular, and Kagome lattices, are either translationally invariant resonant valence bond (RVB) phases with no density-wave order or have coexisting density-wave and RVB orders. We also find that upon increasing the relative strength of hopping and interaction, the translationally invariant Mott states undergo direct second order superfluid-insulator quantum phase transitions. We compute the critical exponents for these transitions and argue using the dual vortex picture that the transitions, when approached through the tip of the Mott lobe, belong to the inverted XY universality class.Comment: 10 pages, 18 figures, minor changes, two references adde

Quantum order by disorder in a spin-one frustrated magnet on the kagome lattice

We study the XXZ spin-one quantum magnet on the kagome lattice as an example where quantum fluctuations on highly degenerate classical ground states lead to various exotic quantum ground states. Previous studies have predicted several quantum phases, but different analytical approaches do not necessarily lead to the same physical picture. In this work, we use Quantum Monte Carlo computations to critically examine some of the predictions made in the string-net mean-field theory and the degenerate perturbation theory combined with duality analysis and effective field theory. It is found that the resulting phase diagram differs from some of the previous predictions. Further implications of our results to different analytical approaches are discussed.Comment: 6 pages, 12 figure

Classical antiferromagnet on a hyperkagome lattice

Motivated by recent experiments on Na_4Ir_3O_8 [Y. Okamoto, M. Nohara, H. Aruga-Katori, and H. Takagi, arXiv:0705.2821 (unpublished)], we study the classical antiferromagnet on a frustrated three-dimensional lattice obtained by selectively removing one of four sites in each tetrahedron of the pyrochlore lattice. This ``hyperkagome'' lattice consists of corner-sharing triangles. We present the results of large-N mean field theory and Monte Carlo computations on O(N) classical spin models. It is found that the classical ground states are highly degenerate. Nonetheless a nematic order emerges at low temperatures in the Heisenberg model (N=3) via ``order by disorder'', representing the dominance of coplanar spin configurations. Implications for ongoing experiments are discussed.Comment: 4 pages, 6 figures, published versio