arXiv subjects

Anders W. Sandvik

Publications and source records attributed to Anders W. Sandvik.

At least 145 records · Page 8Linked to original sources

arXiv2002

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.

cond-mat.str-el↗

arXiv2002

Multi-critical point in a diluted bilayer Heisenberg quantum antiferromagnet

The S=1/2 Heisenberg bilayer antiferromagnet with randomly removed inter-layer dimers is studied using quantum Monte Carlo simulations. A zero-temperature multi-critical point (p*,g*) at the classical percolation density p=p* and inter-layer coupling g* approximately 0.16 is demonstrated. The quantum critical exponents of the percolating cluster are determined using finite-size scaling. It is argued that the associated finite-temperature quantum critical regime extends to zero inter-layer coupling and could be relevant for antiferromagnetic cuprates doped with non-magnetic impurities.

cond-mat.str-el↗

arXiv2002

Classical percolation transition in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet

The two-dimensional antiferromagnetic S=1/2 Heisenberg model with random site dilution is studied using quantum Monte Carlo simulations. Ground state properties of the largest connected cluster on L*L lattices, with L up to 64, are calculated at the classical percolation threshold. In addition, clusters with a fixed number Nc of spins on an infinite lattice at the percolation density are studied for Nc up to 1024. The disorder averaged sublattice magnetization per spin extrapolates to the same non-zero infinite-size value for both types of clusters. Hence, the percolating clusters, which are fractal with dimensionality d=91/48, have antiferromagnetic long-range order. This implies that the order-disorder transition driven by site dilution occurs exactly at the percolation threshold and that the exponents are classical. The same conclusion is reached for the bond-diluted system. The full sublattice magnetization versus site-dilution curve is obtained in terms of a decomposition into a classical geometrical factor and a factor containing all the effects of quantum fluctuations. The spin stiffness is shown to obey the same scaling as the conductivity of a random resistor network.

cond-mat.str-el↗

arXiv2002

Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model

We use a stochastic series expansion quantum Monte Carlo method to study the phase diagram of the one-dimensional extended Hubbard model at half filling for small to intermediate values of the on-site (U) and nearest-neighbor (V) repulsions. We confirm the existence of a novel, long-range-ordered bond-order-wave (BOW) phase recently predicted by Nakamura (J. Phys. Soc. Jpn. 68, 3123 (1999)) in a small region of the parameter space between the familiar charge-density-wave (CDW) state for V > U/2 and the state with dominant spin-density-wave (SDW) fluctuations for V < U/2. We discuss the nature of the transitions among these states and evaluate some of the critical exponents. Further, we determine accurately the position of the multi-critical point, (U_m,V_m)= (4.7 +/- 0.1, 2.51 +/- 0.04) (in energy units where the hopping integral is normalized to unity), above which the two continuous SDW-BOW-CDW transitions are replaced by one discontinuous (first-order) direct SDW-CDW transition. We also discuss the evolution of the CDW and BOW states upon hole doping. We find that in both cases the ground state is a Luther-Emery liquid, i.e., the spin gap remains but the charge gap existing at half-filling is immediately closed upon doping. The charge and bond-order correlations decay with distance r as r^{-K_rho}, where K_rho is approximately 0.5 for the parameters we have considered. We also discuss advantages of using parallel tempering (or exchange Monte Carlo) -- an extended ensemble method that we here combine with quantum Monte Carlo -- in studies of quantum phase transitions.

cond-mat.str-el↗

arXiv2000

Comment on ``Quantum Phase Transition of the Randomly Diluted Heisenberg Antiferromagnet on a Square Lattice''

In Phys. Rev. Lett. 84, 4204 (2000) (cond-mat/9905379), Kato et al. presented quantum Monte Carlo results indicating that the critical concentration of random non-magnetic sites in the two-dimensional antiferromagnetic Heisenberg model equals the classical percolation density; pc=0.407254. The data also suggested a surprising dependence of the critical exponents on the spin S of the magnetic sites, with a gradual approach to the classical percolation exponents as S goes to infinity. I here argue that the exponents in fact are S-independent and equal to those of classical percolation. The apparent S-dependent behavior found by Kato et al. is due to temperature effects in the simulations as well as a quantum effect that masks the true asymptotic scaling behavior for small lattices.

cond-mat.str-el↗

arXiv2000

High-energy magnon dispersion and multi-magnon continuum in the two-dimensional Heisenberg antiferromagnet

We use quantum Monte Carlo simulations and numerical analytic continuation to study high-energy spin excitations in the two-dimensional S=1/2 Heisenberg antiferromagnet at low temperature. We present results for both the transverse and longitudinal dynamic spin structure factor S(q,w) at q=(pi,0) and (pi/2,pi/2). Linear spin-wave theory predicts no dispersion on the line connecting these momenta. Our calculations show that in fact the magnon energy at (pi,0) is 10% lower than at (pi/2,pi/2). We also discuss the transverse and longitudinal multi-magnon continua and their relevance to neutron scattering experiments.

cond-mat.str-el↗

arXiv2000

The sign problem in Monte Carlo simulations of frustrated quantum spin systems

We discuss the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of ``semi-frustrated'' systems (Heisenberg models with ferromagnetic couplings $J_z(r) < 0$ along the $z$-axis and antiferromagnetic couplings $J_{xy}(r)=-J_z(r)$ in the $xy$-plane, for arbitrary distances $r$) the sign problem present for algorithms operating in the $z$-basis can be solved within a recent ``operator-loop'' formulation of the stochastic series expansion method (a cluster algorithm for sampling the diagonal matrix elements of the power series expansion of ${\rm exp}(-βH)$ to all orders). The solution relies on identification of operator-loops which change the configuration sign when updated (``merons'') and is similar to the meron-cluster algorithm recently proposed by Chandrasekharan and Wiese for solving the sign problem for a class of fermion models (Phys. Rev. Lett. {\bf 83}, 3116 (1999)). Some important expectation values, e.g., the internal energy, can be evaluated in the subspace with no merons, where the weight function is positive definite. Calculations of other expectation values require sampling of configurations with only a small number of merons (typically zero or two), with an accompanying sign problem which is not serious. We also discuss problems which arise in applying the meron concept to more general quantum spin models with frustrated interactions.

cond-mat.str-el↗

arXiv1999

The two-dimensional bond-diluted quantum Heisenberg model at the classical percolation threshold

The two-dimensional antiferromagnetic S=1/2 Heisenberg model with random bond dilution is studied using quantum Monte Carlo simulation at the percolation threshold (50% of the bonds removed). Finite-size scaling of the staggered structure factor averaged over the largest connected clusters of sites on L*L lattices shows that long-range order exists within the percolating fractal clusters in the thermodynamic limit. This implies that the order-disorder transition driven by bond-dilution occurs exactly at the percolation threshold and that the exponents are classical. This result should apply also to the site-diluted system.

cond-mat.str-el↗

arXiv1999

Multi-Chain Mean-Field Theory of Quasi One-Dimensional Quantum Spin Systems

A multi-chain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C_0 is modeled by a number of neighbor chains C_d, d = +/-1,...,+/-n, with the edge chains (d=+/-n) coupled to a staggered field. Using a quantum Monte Carlo method, the effective (2n+1)-chain Hamiltonian is solved self-consistently for $n$ up to 4. The results are compared with simulation results for the original Hamiltonian on large rectangular lattices. Both methods show that the staggered magnetization M for small interchain couplings alpha behaves as M=A*alpha^1/2 enhanced by a multiplicative logarithmic correction.

cond-mat.str-el↗

arXiv1999

Ground state parameters, finite-size scaling, and low-temperature properties of the two-dimensional S=1/2 XY model

We present high-precision quantum Monte Carlo results for the S=1/2 XY model on a two-dimensional square lattice, in the ground state as well as at finite temperature. The energy, the spin stiffness, the magnetization, and the susceptibility are calculated and extrapolated to the thermodynamic limit. For the ground state, we test a variety of finite-size scaling predictions of effective Lagrangian theory and find good agreement and consistency between the finite-size corrections for different quantities. The low-temperature behavior of the susceptibility and the internal energy is also in good agreement with theoretical predictions.

cond-mat.stat-mech↗

arXiv1999

Monte Carlo study of a two-dimensional quantum ferromagnet

We present quantum Monte Carlo results for the field and temperature dependence of the magnetization and the spin-lattice relaxation rate $1/T_1$ of a two-dimensional $S=1/2$ quantum Heisenberg ferromagnet. The Monte Carlo method, which yields results free of systematic errors, is described in detail. The high accuracy of the calculated magnetization allows for stringent tests of recent approximate analytical calculations. We also compare our results with recent experimental data for a $ν=1$ quantum Hall ferromagnet, which is expected to be well described by the Heisenberg model. The dynamic response function needed to extract $1/T_1$ is obtained using maximum-entropy analytic continuation of the corresponding imaginary-time dependent correlation function. We discuss the reliability of this approach.

cond-mat.mes-hall↗

arXiv1999

Stochastic series expansion method with operator-loop update

A cluster update (the ``operator-loop'') is developed within the framework of a numerically exact quantum Monte Carlo method based on the power series expansion of exp(-BH) (stochastic series expansion). The method is generally applicable to a wide class of lattice Hamiltonians for which the expansion is positive definite. For some important models the operator-loop algorithm is more efficient than loop updates previously developed for ``worldline'' simulations. The method is here tested on a two-dimensional anisotropic Heisenberg antiferromagnet in a magnetic field.

cond-mat.str-el↗

arXiv1999

Spin-Peierls transition in the Heisenberg chain with finite-frequency phonons

We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond-phonons. Quantum Monte Carlo results for systems with up to N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling alpha exceeds a critical value alpha_c. Using sum rules, we show that the phonon spectral function has divergent (for infinite N) weight extending to zero frequency for alpha < alpha_c. The equal-time phonon-phonon correlations decay with distance r as 1/r. This behavior is characteristic for all 0 < alpha < alpha_c and the q=pi phonon does not soften (to zero frequency) at the transition.

cond-mat.str-el↗

arXiv1998

Possible Exotic Phases in the One-Dimensional Extended Hubbard Model

We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on--site interaction U and a nearest--neighbor interaction V. We focus on the ground state phases of the model in the V >> U region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=V_PS. Using quantum Monte Carlo methods on lattices much larger than in previous Lanczos diagonalization studies, we determine the boundary of phase separation, the Luttinger Liquid correlation exponent K_rho, and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state re-enters from phase separation as the electron density is increased towards half filling. For V < V_PS, our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger Liquid with K_rho < 1, but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger Liquid.

cond-mat.str-el↗

arXiv1998

Two-Dimensional Quantum Ferromagnets

We present 1/N Schwinger boson and quantum Monte Carlo calculations of the magnetization and NMR relaxation rate for the two-dimensional ferromagnetic Heisenberg model representing a quantum Hall system at filling factor nu=1. Comparing the analytic and numerical calculations, we find that the SU(N) version of Schwinger boson theory gives accurate results for the magnetization at low temperatures, whereas the O(N) model works well at higher temperatures.

cond-mat.mes-hall↗

arXiv1997

The role of winding numbers in quantum Monte Carlo simulations

We discuss the effects of fixing the winding number in quantum Monte Carlo simulations. We present a simple geometrical argument as well as strong numerical evidence that one can obtain exact ground state results for periodic boundary conditions without changing the winding number. However, for very small systems the temperature has to be considerably lower than in simulations with fluctuating winding numbers. The relative deviation of a calculated observable from the exact ground state result typically scales as $T^γ$, where the exponent $γ$ is model and observable dependent and the prefactor decreases with increasing system size. Analytic results for a quantum rotor model further support our claim.

cond-mat.stat-mech↗

arXiv1995

NMR relaxation rates for the spin-1/2 Heisenberg chain

The spin-lattice relaxation rate $1/T_1$ and the spin echo decay rate $1/T_{2G}$ for the spin-$1\over 2$ antiferromagnetic Heisenberg chain are calculated using quantum Monte Carlo and maximum entropy analytic continuation. The results are compared with recent analytical calculations by Sachdev. If the nuclear hyperfine form factor $A_q$ is strongly peaked around $q=π$ the predicted low-temperature behavior [$1/T_1 \sim \ln{^{1/2}(1/T)}$, $1/T_{2G} \sim \ln{^{1/2}(1/T)}/\sqrt{T}$] extends up to temperatures as high as $T/J \approx 0.5$. If $A_q$ has significant weight for $q \approx 0$ there are large contributions from diffusive long-wavelength processes not taken into account in the theory, and very low temperatures are needed in order to observe the asymptotic $T \to 0$ forms.

cond-mat↗

arXiv1995

Quantum-Critical Behavior in a Two-Layer Antiferromagnet

We analyze quantum Monte Carlo data in the vicinity of the quantum transition between a Neel state and a quantum paramagnet in a two-layer, square lattice spin 1/2 Heisenberg antiferromagnet. The real-space correlation function and the universal amplitude ratio of the structure factor and the dynamic susceptibility show clear evidence of quantum critical behavior at low temperatures. The numerical results are in good quantitative agreement with $1/N$ calculations for the $O(N)$ non-linear sigma model. A discrepancy, reported earlier, between the critical properties of the antiferromagnet and the sigma model is resolved. We also discuss the values of prefactors of the dynamic susceptibility and the structure factor in a single layer antiferromagnet at low $T$.

cond-mat↗