Loop algorithm for classical Heisenberg models with spin-ice type degeneracy

In many frustrated Ising models, a single-spin flip dynamics is frozen out at low temperatures compared to the dominant interaction energy scale because of the discrete "multiple valley" structure of degenerate ground-state manifold. This makes it difficult to study low-temperature physics of these frustrated systems by using Monte Carlo simulation with the standard single-spin flip algorithm. A typical example is the so-called spin ice model, frustrated ferromagnets on the pyrochlore lattice. The difficulty can be avoided by a global-flip algorithm, the loop algorithm, that enables to sample over the entire discrete manifold and to investigate low-temperature properties. We extend the loop algorithm to Heisenberg spin systems with strong easy-axis anisotropy in which the ground-state manifold is continuous but still retains the spin-ice type degeneracy. We examine different ways of loop flips and compare their efficiency. The extended loop algorithm is applied to the following two models, a Heisenberg antiferromagnet with easy-axis anisotropy along the z axis, and a Heisenberg spin ice model with the local easy-axis anisotropy. For both models, we demonstrate high efficiency of our loop algorithm by revealing the low-temperature properties which were hard to access by the standard single-spin flip algorithm. For the former model, we examine the possibility of order-from-disorder and critically check its absence. For the latter model, we elucidate a gas-liquid-solid transition, namely, crossover or phase transition among paramagnet, spin-ice liquid, and ferromagnetically-ordered ice-rule state.Comment: 12 pages, 11 figures, accepted for publication in Phys. Rev.

Semiclassical spin liquid state of easy axis Kagome antiferromagnets

Motivated by recent experiments on Nd-langasite, we consider the effect of strong easy axis single-ion anisotropy $D$ on $S > 3/2$ spins interacting with antiferromagnetic exchange $J$ on the Kagome lattice. When $T \ll DS^2$, the collinear low energy states selected by the anisotropy map on to configurations of the classical Kagome lattice Ising antiferromagnet. However, the low temperature limit is quite different from the cooperative Ising paramagnet that obtains classically for $T \ll JS^2$. We find that sub-leading ${\mathcal O}(J^3S/D^2)$ multi-spin interactions arising from the transverse quantum dynamics result in a crossover from an intermediate temperature classical cooperative Ising paramagnet to a semiclassical spin liquid with distinct short-ranged correlations for $T \ll J^3S/D^2$.Comment: 4 pages, 3 eps figure

Classical dimer model with anisotropic interactions on the square lattice

We discuss phase transitions and the phase diagram of a classical dimer model with anisotropic interactions defined on a square lattice. For the attractive region, the perturbation of the orientational order parameter introduced by the anisotropy causes the Berezinskii-Kosterlitz-Thouless transitions from a dimer-liquid to columnar phases. According to the discussion by Nomura and Okamoto for a quantum-spin chain system [J. Phys. A 27, 5773 (1994)], we proffer criteria to determine transition points and also universal level-splitting conditions. Subsequently, we perform numerical diagonalization calculations of the nonsymmetric real transfer matrices up to linear dimension specified by L=20 and determine the global phase diagram. For the repulsive region, we find the boundary between the dimer-liquid and the strong repulsion phases. Based on the dispersion relation of the one-string motion, which exhibits a two-fold ``zero-energy flat band'' in the strong repulsion limit, we give an intuitive account for the property of the strong repulsion phase.Comment: 11 pages, 8 figure

Quantum Monte Carlo study of the transverse-field Ising model on a frustrated checkerboard lattice

We present the numerical results for low temperature behavior of the transverse-field Ising model on a frustrated checkerboard lattice, with focus on the effect of both quantum and thermal fluctuations. Applying the recently-developed continuous-time quantum Monte Carlo algorithm, we compute the magnetization and susceptibility down to extremely low temperatures while changing the magnitude of both transverse and longitudinal magnetic fields. Several characteristic behaviors are observed, which were not inferred from the previously studied quantum order from disorder at zero temperature, such as a horizontal-type stripe ordering at a substantial longitudinal field and a persistent critical behavior down to low temperature in a weak longitudinal field region.Comment: 6 pages, 5 figures, accepted for publication in J. Phys.: Conf. Se

Nonintegrability of the two-body problem in constant curvature spaces

We consider the reduced two-body problem with the Newton and the oscillator potentials on the sphere ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For both types of interaction we prove the nonexistence of an additional meromorphic integral for the complexified dynamic systems.Comment: 20 pages, typos correcte

Numerical Linked-Cluster Approach to Quantum Lattice Models

We present a novel algorithm that allows one to obtain temperature dependent properties of quantum lattice models in the thermodynamic limit from exact diagonalization of small clusters. Our Numerical Linked Cluster (NLC) approach provides a systematic framework to assess finite-size effects and is valid for any quantum lattice model. Unlike high temperature expansions (HTE), which have a finite radius of convergence in inverse temperature, these calculations are accurate at all temperatures provided the range of correlations is finite. We illustrate the power of our approach studying spin models on {\it kagom\'e}, triangular, and square lattices.Comment: 4 pages, 5 figures, published versio

Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets

When one tries to simulate quantum spin systems by the Monte Carlo method, often the 'minus-sign problem' is encountered. In such a case, an application of probabilistic methods is not possible. In this paper the method has been proposed how to avoid the minus sign problem for certain class of frustrated Heisenberg models. The systems where this method is applicable are, for instance, the pyrochlore lattice and the $J_1-J_2$ Heisenberg model. The method works in singlet sector. It relies on expression of wave functions in dimer (pseudo)basis and writing down the Hamiltonian as a sum over plaquettes. In such a formulation, matrix elements of the exponent of Hamiltonian are positive.Comment: 19 LaTeX pages, 6 figures, 1 tabl

Antiferromagnetic Quantum Spins on the Pyrochlore Lattice

The ground state of the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice is theoretically investigated. Starting from the limit of isolated tetrahedra, I include interactions between the tetrahedra and obtain an effective model for the spin-singlet ground state multiplet by third-order perturbation. I determine its ground state using the mean-field approximation and found a dimerized state with a four-sublattice structure, which agrees with the proposal by Harris et al. I also discuss chirality correlations and spin correlations for this state.Comment: 4 pages in 2-column format, 5 figures; To appear in J. Phys. Soc. Jpn. (Mar, 2001