Single particle spectrum of the flux phase in the FM Kondo Model

We investigate the 2D ferromagnetic Kondo lattice model for manganites with classical corespins at Hund's rule coupling J_H=6, with antiferromagnetic superexchange 0.03 < J' < 0.05. We employ canonical and grand canonical unbiased Monte Carlo simulations and find paramagnetism, weak ferromagnetism and the Flux phase, depending on doping and on J'. The observed single particle spectrum in the flux phase differs from the idealized infinite lattice case, but agrees well with an idealized finite lattice case with thermal fluctuations.Comment: contribution to the SCES04 conferenc

Reduction of the sign problem using the meron-cluster approach

The sign problem in quantum Monte Carlo calculations is analyzed using the meron-cluster solution. The concept of merons can be used to solve the sign problem for a limited class of models. Here we show that the method can be used to \textit{reduce} the sign problem in a wider class of models. We investigate how the meron solution evolves between a point in parameter space where it eliminates the sign problem and a point where it does not affect the sign problem at all. In this intermediate regime the merons can be used to reduce the sign problem. The average sign still decreases exponentially with system size and inverse temperature but with a different prefactor. The sign exhibits the slowest decrease in the vicinity of points where the meron-cluster solution eliminates the sign problem. We have used stochastic series expansion quantum Monte Carlo combined with the concept of directed loops.Comment: 8 pages, 9 figure

Electrically and Magnetically Charged States and Particles in the 2+1-Dimensional Z_N-Higgs Gauge Model

Electrically as well as magnetically charged states are constructed in the 2+1-dimensional Euclidean Z_N-Higgs lattice gauge model, the former following ideas of Fredenhagen and Marcu and the latter using duality transformations on the algebra of observables. The existence of electrically and of magnetically charged particles is also established. With this work we prepare the ground for the constructive study of anyonic statistics of multiparticle scattering states of electrically and magnetically charged particles in this model (work in progress).Comment: 57 pages, Sfb 288 Preprint No. 109. To appear in Commun. Math. Phys. About the file: This is a uuencoded, "gzip-ed" postscript file. It is about 300kB large. The original ps file is about 700kB large. All figures are included. The LaTeX sources ou even hard copies can be required to the authors at [email protected] or Freie Universitaet Berlin. Institut fuer Theoretische Physik. Arnimallee 14. Berlin 14195 German

Directed geometrical worm algorithm applied to the quantum rotor model

We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm Monte Carlo updates are made through the biased reptation of a worm through the lattice. A directed algorithm is an algorithm where, during the construction of the worm, the probability for erasing the immediately preceding part of the worm, when adding a new part,is minimal. We introduce a simple numerical procedure for minimizing this probability. The procedure only depends on appropriately defined local probabilities and should be generally applicable. Furthermore we show how correlation functions, C(r,tau) can be straightforwardly obtained from the probability of a worm to reach a site (r,tau) away from its starting point independent of whether or not a directed version of the algorithm is used. Detailed analytical proofs of the validity of the Monte Carlo algorithms are presented for both the directed and un-directed geometrical worm algorithms. Results for auto-correlation times and Green functions are presented for the quantum rotor model.Comment: 11 pages, 9 figures, v2 : Additional results and data calculated at an incorrect chemical potential replaced. Conclusions unchange

Coarse-grained loop algorithms for Monte Carlo simulation of quantum spin systems

Recently, Syljuasen and Sandvik proposed a new framework for constructing algorithms of quantum Monte Carlo simulation. While it includes new classes of powerful algorithms, it is not straightforward to find an efficient algorithm for a given model. Based on their framework, we propose an algorithm that is a natural extension of the conventional loop algorithm with the split-spin representation. A complete table of the vertex density and the worm-scattering probability is presented for the general XXZ model of an arbitrary S with a uniform magnetic field.Comment: 12 pages, 7 figures, insert a word "squared" in the first line of the caption of Fig.7 and correct the label of vertical axis of Fig.

A Cluster Method for the Ashkin--Teller Model

A cluster Monte Carlo algorithm for the Ashkin-Teller (AT) model is constructed according to the guidelines of a general scheme for such algorithms. Its dynamical behaviour is tested for the square lattice AT model. We perform simulations on the line of critical points along which the exponents vary continuously, and find that critical slowing down is significantly reduced. We find continuous variation of the dynamical exponent $z$ along the line, following the variation of the ratio $\alpha/\nu$, in a manner which satisfies the Li-Sokal bound $z_{cluster}\geq\alpha/\nu$, that was so far proved only for Potts models.Comment: 18 pages, Revtex, figures include

Cluster Monte Carlo Simulations of the Nematic--Isotropic Transition

We report the results of simulations of the Lebwohl-Lasher model of the nematic-isotropic transition using a new cluster Monte Carlo algorithm. The algorithm is a modification of the Wolff algorithm for spin systems, and greatly reduces critical slowing down. We calculate the free energy in the neighborhood of the transition for systems up to linear size 70. We find a double well structure with a barrier that grows with increasing system size, obeying finite size scaling for systems of size greater than 35. We thus obtain an estimate of the value of the transition temperature in the thermodynamic limit.Comment: 4 figure

Magnetization process of the spin-1/2 XXZ models on square and cubic lattices

The magnetization process of the spin-1/2 antiferromagnetic XXZ model with Ising-like anisotropy in the ground state is investigated. We show numerically that the Ising-like XXZ models on square and cubic lattices show a first-order phase transition at some critical magnetic field. We estimate the value of the critical field and the magnetization jump on the basis of the Maxwell construction. The magnetization jump in the Ising-limit is investigated by means of perturbation theory. Based on our numerical results, we briefly discuss the phase diagram of the extended Bose-Hubbard model in the hard-core limit.Comment: 13 pages, RevTex, 7 PostScript figures, to appear in Phys.Rev.

A Theory of Ferroelectric Phase Transition in SrTiO3_3 induced by Isotope Replacement

A theory to describe the dielectric anomalies and the ferroelectric phase transition induced by oxygen isotope replacement in SrTiO$_3$ is developed. The proposed model gives consistent explanation between apparently contradictory experimental results on macroscopic dielectric measurements versus microscopic lattice dynamical measurements by neutron scattering studies. The essential feature is described by a 3-state quantum order-disorder system characterizing the degenerated excited states in addition to the ground state of TiO$_6$ cluster. The effect of isotope replacement is taken into account through the tunneling frequency between the excited states. The dielectric properties are analyzed by the mean field approximation (MFA), which gives qualitative agreements with experimental results throughout full range of the isotope concentration.The phase diagram in the temperature-tunneling frequencycoordinate is studied by a QMC method to confirm the qualitative validity of the MFA analysis.Comment: 26 pages, 8 figure

Vortex behavior near a spin vacancy in 2D XY-magnets

The dynamical behavior of anisotropic two dimensional Heisenberg models is still a matter of controversy. The existence of a central peak at all temperatures and a rich structure of magnon peaks are not yet understood. It seems that the central peaks are related, in some way, to structures like vortices. In order to contribute to the discussion of the dynamical behavior of the model we use Monte Carlo and spin dynamics simulations as well analytical calculations to study the behavior of vortices in the presence of nonmagnetic impurities. Our simulations show that vortices are attracted and trapped by the impurities. Using this result we show that if we suppose that vortices are not very much disturbed by the presence of the impurities, then they work as an attractive potential to the vortices explaining the observed behavior in our simulations.Comment: 4 pages, 6 figure