Hans Gerd Evertz

The ALPS project release 2.0: open source software for strongly correlated systems

We present release 2.0 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. The code development is centered on common XML and HDF5 data formats, libraries to simplify and speed up code development, common evaluation and plotting tools, and simulation programs. The programs enable non-experts to start carrying out serial or parallel numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), the density matrix renormalization group (DMRG) both in a static version and a dynamic time-evolving block decimation (TEBD) code, and quantum Monte Carlo solvers for dynamical mean field theory (DMFT). The ALPS libraries provide a powerful framework for programmers to develop their own applications, which, for instance, greatly simplify the steps of porting a serial code onto a parallel, distributed memory machine. Major changes in release 2.0 include the use of HDF5 for binary data, evaluation tools in Python, support for the Windows operating system, the use of CMake as build system and binary installation packages for Mac OS X and Windows, and integration with the VisTrails workflow provenance tool. The software is available from our web server at http://alps.comp-phys.org/.

Cluster algorithm for vertex models

We present a new type of cluster algorithm that strongly reduces critical slowing down in simulations of vertex models. Since the clusters are closed paths of bonds, we call it the loop algorithm. The basic steps in constructing a cluster are the breakup and the freezing of vertices. We concentrate on the case of the F model, which is a subset of the six-vertex model exhibiting a Kosterlitz-Thouless transition. The loop algorithm is also applicable to simulations of other vertex models and of one- and two-dimensional quantum spin systems

The loop algorithm

A review of the loop algorithm , its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a quantum Monte Carlo procedure that employs non-local changes of worldline configurations, determined by local stochastic decisions. It is based on a formulation of quantum models of any dimension in an extended ensemble of worldlines and graphs, and is related to Swendsen-Wang algorithms. It can be represented directly on an operator level, both with a continuous imaginary time path integral and with the stochastic series expansion. It overcomes many of the difficulties of traditional worldline simulations. Autocorrelations are reduced by orders of magnitude. Grand-canonical ensembles, off-diagonal operators, and variance reduced estimators are accessible. In some cases, infinite systems can be simulated. For a restricted class of models, the fermion sign problem can be overcome. Transverse magnetic fields are handled efficiently, in contrast to strong diagonal fields. The method has been applied successfully to a variety of models for spin and charge degrees of freedom, including Heisenberg and XYZ spin models, hard-core bosons, Hubbard and t - J -models. Owing to the improved efficiency, precise calculations of asymptotic behaviour and of quantum critical exponents have been possible.

Tricritical point in lattice QED

Abstract The four-dimensional U(1) lattice gauge theory with the action − Σ p ( γ cos 2 θ p + γ cos 2 θ p ) is studied by Monte Carlo simulation along the phase transition line separating the confinement and the Coulomb phases. The discontinuity of 〈cos θ p 〉, determined in the interval 0.2 ⩽ γ ⩽ 0.5, is extrapolated according to a power law and shown to vanish at the tricritical point β TCP = ±449, γ TCP =−0.11±0.05 (errors are systematic). A negative value of γ TCP means that the phase transition in lattice QED with Wilson action ( γ = 0) is of first order.

Critical dynamics in the two-dimensional classical XY model: A spin-dynamics study.

Using spin-dynamics techniques we have performed large-scale computer simulations of the dynamic behavior of the classical three component XY-model (i.e. the anisotropic limit of an easy-plane Heisenberg ferromagnet), on square lattices of size up to 192^2, for several temperatures below, at, and above T_KT. The temporal evolution of spin configurations was determined numerically from coupled equations of motion for individual spins by a fourth order predictor-corrector method, with initial spin configurations generated by a hybrid Monte Carlo algorithm. The neutron scattering function S(q,omega) was calculated from the resultant space-time displaced spin-spin correlation function. Pronounced spin-wave peaks were found both in the in-plane and the out-of-plane scattering function over a wide range of temperatures. The in-plane scattering function S^xx also has a large number of clear but weak additional peaks, which we interpret to come from two-spin-wave scattering. In addition, we observed a small central peak in S^xx, even at temperatures well below the phase transition. We used dynamic finite size scaling theory to extract the dynamic critical exponent z. We find z=1.00(4) for all T <= T_KT, in excellent agreement with theoretical predictions, although the shape of S(q,omega) is not well described by current theory.

PSEUDOGAPS AND THEIR INTERPLAY WITH MAGNETIC EXCITATIONS IN THE DOPED 2D HUBBARD MODEL

On the basis of quantum Monte Carlo simulations of the two-dimensional Hubbard model which cover the doping range from the underdoped to the overdoped regime, we find that the single-particle spectral weight A({rvec k},{omega}) qualitatively reproduces both the momentum (d{sub x{sup 2}{minus}y{sup 2}} symmetry) and doping dependence of the pseudogap as found in photoemission experiments. The drastic doping dependence of the spin response {chi}{sub s}({rvec q},{omega}), which is sharp in both {rvec q}[{approx}({pi},{pi})] and {omega} in the underdoped regime but broad and structureless otherwise, identifies remnants of the antiferromagnetic order as the driving mechanism behind the pseudogap and its evolution with doping. {copyright} {ital 1997} {ital The American Physical Society}

Finite temperature SU(2) Higgs model on a lattice

Abstract By means of Monte Carlo simulations we investigate the finite temperature SU(2) lattice Higgs model with a doublet scalar field at large but finite quartic self-coupling. The lattices are asymmetric in space and time extensions and their spatial size is varied in order to study finite size effects. The second order deconfinement transition at high temperature of the pure SU(2) gauge theory changes into a crossover when the scalar field is coupled to the gauge field. The Higgs phase transition at zero temperature also changes into a crossover when the temperature gets high enough. Its position shifts slightly to larger values of the hopping parameter. This means that in the Higgs region of the phase diagram the system passes through this crossover when the temperature is raised at fixed values of the coupling parameters, in analogy to the symmetry restoring transition of Kirzhnits, Linde and Weinberg in the standard model.

SU(2) Higgs Boson and vector Boson masses on the lattice

Results are presented for the masses mH and mW of isoscalar and isovector states in the lattice SU(2) Higgs model with scalar field in the fundamental representation. The Monte Carlo study is done on a lattice of size 83 × 16 in the vicinity of three points of the Higgs-phase-transition sheet. The masses show only weak dependence on the quartic self-coupling λ and on the gauge coupling β, but an interesting dependence on the hopping parameter κ. At the phase transition mH has a sharp dip consistent with critical behaviour, whereas mW stays above 12a. The mass ratio mHmW becomes larger than one in the Higgs region shortly above the phase transition.

Stochastic cluster algorithms for discrete gaussian (SOS) models

Abstract We present new Monte Carlo cluster algorithms which eliminate critical slowing down in the simulation of solid-on-solid models. In this letter we focus on the two-dimensional discrete gaussian model. The algorithms are based on reflecting the integer valued spin variables with respect to appropriately chosen reflection planes. The proper choice of the reflection plane turns out to be crucial in order to obtain a small dynamical exponent z . Actually, the successful versions of our algorithm are a mixture of two different procedures for choosing the reflection plane, one of them ergodic but slow, the other one non-ergodic and also slow when combined with a Metropolis algorithm.

PHOTON AND BOSONIUM MASSES IN SCALAR LATTICE QED

We analyze the particle spectrum of the compact U(1) lattice gauge theory with a scalar matter field of unit charge. The nonperturbative Monte Carlo calculation is performed on lattices of sizes 83 × 16, 124 and 164. In the Coulomb phase we find a massless photon and massive scalar and vector bosonium states which are neutral bound states of charged bosonic particles, analogous to the positronium in QED. In the Higgs region of the confinement-Higgs phase the massive photon and the Higgs boson are present. Here we do not find any other vector state with a mass substantially different from the photon mass.