57 research outputs found
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Aruga-Katori, and H. Takagi, arXiv:0705.2821 (unpublished)], we study the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
N\'eel to dimer transition in spin-S antiferromagnets: Comparing bond operator theory with quantum Monte Carlo simulations for bilayer Heisenberg models
We study the N\'eel to dimer transition driven by interlayer exchange
coupling in spin-S Heisenberg antiferromagnets on bilayer square and honeycomb
lattices for S=1/2, 1, 3/2. Using exact stochastic series expansion quantum
Monte Carlo (QMC) calculations, we find that the critical value of the
interlayer coupling, J_{\perp c}[S], increases with increasing S, with clear
evidence that the transition is in the O(3) universality class for all S. Using
bond operator mean field theory restricted to singlet and triplet states, we
find J_{\perp c}[S] ~ S(S+1), in qualitative accord with QMC, but the resulting
J_{\perp c} [S] is significantly smaller than the QMC value. For S=1/2,
incorporating triplet-triplet interactions within a variational approach yields
a critical interlayer coupling which agrees well with QMC. For higher spin, we
argue that it is crucial to account for the high energy quintet modes, and show
that including these within a perturbative scheme leads to reasonable agreement
with QMC results for S=1,3/2. We discuss the broad implications of our results
for systems such as the triangular lattice S=1 dimer compound Ba_3Mn_2O_8 and
the S=3/2 bilayer honeycomb material Bi_3Mn_4O_{12}(NO_{3}).Comment: 14 pages, 7 figures, 2 tables. Updated data, corrected typos, added
two paragraph
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