Loop algorithm for Heisenberg models with biquadratic interaction and phase transitions in two dimensions

We present a new algorithm for quantum Monte Carlo simulation based on global updating with loops. While various theoretical predictions are confirmed in one dimension, we find, for S=1 systems on a square lattice with an antiferromagnetic biquadratic interaction, that the intermediate phase between the antiferromagnetic and the ferromagnetic phases is disordered and that the two phase transitions are both of the first order in contrast to the one-dimensional case. It is strongly suggested that the transition points coincide those at which the algorithm changes qualitatively.Comment: 4 pages including 4 figures, to appear in JPS

Recent Developments of World-Line Monte Carlo Methods

World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms -- the loop algorithm, the worm algorithm, and the directed-loop algorithm -- for updating world-line configurations are presented in a unified perspective. Detailed descriptions of the algorithms in specific cases are also given.Comment: To appear in Journal of Physical Society of Japa

Nematic, vector-multipole, and plateau-liquid states in the classical O(3) pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field

The classical bilinear-biquadratic nearest-neighbor Heisenberg antiferromagnet on the pyrochlore lattice does not exhibit conventional Neel-type magnetic order at any temperature or magnetic field. Instead spin correlations decay algebraically over length scales r ~ \sqrt{T}, behavior characteristic of a Coulomb phase arising from a strong local constraint. Despite this, its thermodynamic properties remain largely unchanged if Neel order is restored by the addition of a degeneracy-lifting perturbation, e.g., further neighbor interactions. Here we show how these apparent contradictions can be resolved by a proper understanding of way in which long-range Neel order emerges out of well-formed local correlations, and identify nematic and vector-multipole orders hidden in the different Coulomb phases of the model. So far as experiment is concerned, our results suggest that where long range interactions are unimportant, the magnetic properties of Cr spinels which exhibit half-magnetization plateaux may be largely independent of the type of magnetic order present.Comment: 27 pages latex, 25 eps figure

Order from structural disorder in XYXY pyrochlore antiferromagnet Er2Ti2O7\rm Er_2Ti_2O_7

Effect of structural disorder is investigated for an $XY$ pyrochlore antiferromagnet with continuous degeneracy of classical ground states. Two types of disorder, vacancies and weakly fluctuating exchange bonds, lift degeneracy selecting the same subset of classical ground states. Analytic and numerical results demonstrate that such an "order by structural disorder" mechanism competes with the effect of thermal and quantum fluctuations. Our theory predicts that a small amount of nonmagnetic impurities in $\rm{Er_2Ti_2O_7}$ will stabilize the coplanar $\psi_3$ ($m_{x^2-y^2}$) magnetic structure as opposed to the $\psi_2$ ($m_{3z^2-r^2}$) state found in pure material

Superconductivity in model cuprate as an S=1 pseudomagnon condensation

We make use of the S=1 pseudospin formalism to describe the charge degree of freedom in a model high-$T_c$ cuprate with the on-site Hilbert space reduced to the three effective valence centers, nominally Cu$^{1+,\,2+,\,3+}$. Starting with a parent cuprate as an analogue of the quantum paramagnet ground state and using the Schwinger boson technique we found the pseudospin spectrum and conditions for the pseudomagnon condensation with phase transition to a superconducting state.Comment: Version to be published in JLT

Global phase diagram of the spin-1 antiferromagnet with uniaxial anisotropy on the kagome lattice

The phase diagram of the XXZ spin-1 quantum magnet on the kagome lattice is studied for all cases where the $J_z$ coupling is antiferromagnetic. In the zero magnetic field case, the six previously introduced phases, found using various methods, are: the nondegenerate gapped photon phase which breaks no space symmetry or spin symmetry; the six-fold degenerate phase with plaquette order, which breaks both time reversal symmetry and translational symmetry; the "superfluid" (ferromagnetic) phase with an in-plane global U(1) symmetry broken, when $J_{xy} 0$; the nematic phase when $D < 0$ and large; and a phase with resonating dimers on each hexagon. We obtain all of these phases and partial information about their quantum phase transitions in a single framework by studying condensation of defects in the six-fold plaquette phases. The transition between nematic phase and the six-fold degenerate plaquette phase is potentially an unconventional second-order critical point. In the case of a nonzero magnetic field along $\hat{z}$, another ordered phase with translation symmetry broken is opened up in the nematic phase. Due to the breaking of time-reversal symmetry by the field, a supersolid phase emerges between the six-fold plaquette order and the superfluid phase. This phase diagram might be accessible in nickel compounds, BF$_4$ salts, or optical lattices of atoms with three degenerate states on every site.Comment: 17 pages, 16 figure