Anisotropic two-dimensional Heisenberg model by Schwinger-boson Gutzwiller projected method

Two-dimensional Heisenberg model with anisotropic couplings in the $x$ and $y$ directions ($J_x \neq J_y$) is considered. The model is first solved in the Schwinger-boson mean-field approximation. Then the solution is Gutzwiller projected to satisfy the local constraint that there is only one boson at each site. The energy and spin-spin correlation of the obtained wavefunction are calculated for systems with up to $20 \times 20$ sites by means of the variational Monte Carlo simulation. It is shown that the antiferromagnetic long-range order remains down to the one-dimensional limit.Comment: 15 pages RevTex3.0, 4 figures, available upon request, GWRVB8-9

The Debye-Waller Factor in solid 3He and 4He

The Debye-Waller factor and the mean-squared displacement from lattice sites for solid 3He and 4He were calculated with Path Integral Monte Carlo at temperatures between 5 K and 35 K, and densities between 38 nm^(-3) and 67 nm^(-3). It was found that the mean-squared displacement exhibits finite-size scaling consistent with a crossover between the quantum and classical limits of N^(-2/3) and N^(-1/3), respectively. The temperature dependence appears to be T^3, different than expected from harmonic theory. An anisotropic k^4 term was also observed in the Debye-Waller factor, indicating the presence of non-Gaussian corrections to the density distribution around lattice sites. Our results, extrapolated to the thermodynamic limit, agree well with recent values from scattering experiments.Comment: 5 figure

Transfer-Matrix Monte Carlo Estimates of Critical Points in the Simple Cubic Ising, Planar and Heisenberg Models

The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the statistical noise can be reduced considerably by a similarity transformation of the transfer matrix using a variational estimate of its leading eigenvector, in analogy with a common practice in various quantum Monte Carlo techniques. Here we take the two-dimensional coupled $XY$-Ising model as an example. Furthermore, we calculate interface free energies of finite three-dimensional O($n$) models, for the three cases $n=1$, 2 and 3. Application of finite-size scaling to the numerical results yields estimates of the critical points of these three models. The statistical precision of the estimates is satisfactory for the modest amount of computer time spent

Comparison of two non-primitive methods for path integral simulations: Higher-order corrections vs. an effective propagator approach

Two methods are compared that are used in path integral simulations. Both methods aim to achieve faster convergence to the quantum limit than the so-called primitive algorithm (PA). One method, originally proposed by Takahashi and Imada, is based on a higher-order approximation (HOA) of the quantum mechanical density operator. The other method is based upon an effective propagator (EPr). This propagator is constructed such that it produces correctly one and two-particle imaginary time correlation functions in the limit of small densities even for finite Trotter numbers P. We discuss the conceptual differences between both methods and compare the convergence rate of both approaches. While the HOA method converges faster than the EPr approach, EPr gives surprisingly good estimates of thermal quantities already for P = 1. Despite a significant improvement with respect to PA, neither HOA nor EPr overcomes the need to increase P linearly with inverse temperature. We also derive the proper estimator for radial distribution functions for HOA based path integral simulations.Comment: 17 pages, latex, 6 postscript figure

Thermodynamics of Random Ferromagnetic Antiferromagnetic Spin-1/2 Chains

Using the quantum Monte Carlo Loop algorithm, we calculate the temperature dependence of the uniform susceptibility, the specific heat, the correlation length, the generalized staggered susceptibility and magnetization of a spin-1/2 chain with random antiferromagnetic and ferromagnetic couplings, down to very low temperatures. Our data show a consistent scaling behavior in all the quantities and support strongly the conjecture drawn from the approximate real-space renormalization group treatment.A statistical analysis scheme is developed which will be useful for the search of scaling behavior in numerical and experimental data of random spin chains.Comment: 13 pages, 13 figures, RevTe

Variational Monte Carlo study of the ground state properties and vacancy formation energy of solid para-H2 using a shadow wave function

A Shadow Wave Function (SWF) is employed along with Variational Monte Carlo techniques to describe the ground state properties of solid molecular para-hydrogen. The study has been extended to densities below the equilibrium value, to obtain a parameterization of the SWF useful for the description of inhomogeneous phases. We also present an estimate of the vacancy formation energy as a function of the density, and discuss the importance of relaxation effects near the vacant site

Random Exchange Quantum Heisenberg Chains

The one-dimensional quantum Heisenberg model with random $\pm J$ bonds is studied for $S=\frac{1}{2}$ and $S=1$. The specific heat and the zero-field susceptibility are calculated by using high-temperature series expansions and quantum transfer matrix method. The susceptibility shows a Curie-like temperature dependence at low temperatures as well as at high temperatures. The numerical results for the specific heat suggest that there are anomalously many low-lying excitations. The qualitative nature of these excitations is discussed based on the exact diagonalization of finite size systems.Comment: 13 pages, RevTex, 12 figures available on request ([email protected]

Nature of the quantum phase transitions in the two-dimensional hardcore boson model

We use two Quantum Monte Carlo algorithms to map out the phase diagram of the two-dimensional hardcore boson Hubbard model with near ($V_1$) and next near ($V_2$) neighbor repulsion. At half filling we find three phases: Superfluid (SF), checkerboard solid and striped solid depending on the relative values of $V_1$, $V_2$ and the kinetic energy. Doping away from half filling, the checkerboard solid undergoes phase separation: The superfluid and solid phases co-exist but not as a single thermodynamic phase. As a function of doping, the transition from the checkerboard solid is therefore first order. In contrast, doping the striped solid away from half filling instead produces a striped supersolid phase: Co-existence of density order with superfluidity as a single phase. One surprising result is that the entire line of transitions between the SF and checkerboard solid phases at half filling appears to exhibit dynamical O(3) symmetry restoration. The transitions appear to be in the same universality class as the special Heisenberg point even though this symmetry is explicitly broken by the $V_2$ interaction.Comment: 10 pages, 14 eps figures, include

Quantum Monte Carlo with Directed Loops

We introduce the concept of directed loops in stochastic series expansion and path integral quantum Monte Carlo methods. Using the detailed balance rules for directed loops, we show that it is possible to smoothly connect generally applicable simulation schemes (in which it is necessary to include back-tracking processes in the loop construction) to more restricted loop algorithms that can be constructed only for a limited range of Hamiltonians (where back-tracking can be avoided). The "algorithmic discontinuities" between general and special points (or regions) in parameter space can hence be eliminated. As a specific example, we consider the anisotropic S=1/2 Heisenberg antiferromagnet in an external magnetic field. We show that directed loop simulations are very efficient for the full range of magnetic fields (zero to the saturation point) and anisotropies. In particular for weak fields and anisotropies, the autocorrelations are significantly reduced relative to those of previous approaches. The back-tracking probability vanishes continuously as the isotropic Heisenberg point is approached. For the XY-model, we show that back-tracking can be avoided for all fields extending up to the saturation field. The method is hence particularly efficient in this case. We use directed loop simulations to study the magnetization process in the 2D Heisenberg model at very low temperatures. For LxL lattices with L up to 64, we utilize the step-structure in the magnetization curve to extract gaps between different spin sectors. Finite-size scaling of the gaps gives an accurate estimate of the transverse susceptibility in the thermodynamic limit: chi_perp = 0.0659 +- 0.0002.Comment: v2: Revised and expanded discussion of detailed balance, error in algorithmic phase diagram corrected, to appear in Phys. Rev.

Measurement of the partial widths of the Z into up- and down-type quarks

Using the entire OPAL LEP1 on-peak Z hadronic decay sample, Z -> qbarq gamma decays were selected by tagging hadronic final states with isolated photon candidates in the electromagnetic calorimeter. Combining the measured rates of Z -> qbarq gamma decays with the total rate of hadronic Z decays permits the simultaneous determination of the widths of the Z into up- and down-type quarks. The values obtained, with total errors, were Gamma u = 300 ^{+19}_{-18} MeV and Gamma d = 381 ^{+12}_{-12} MeV. The results are in good agreement with the Standard Model expectation.Comment: 22 pages, 5 figures, Submitted to Phys. Letts.