105 research outputs found
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 along the -axis
and antiferromagnetic couplings in the -plane, for
arbitrary distances ) the sign problem present for algorithms operating in
the -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
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.Comment: 13 pages, 16 figure
Order-Disorder Transition in a Two-Layer Quantum Antiferromagnet
We have studied the antiferromagnetic order -- disorder transition occurring
at in a 2-layer quantum Heisenberg antiferromagnet as the inter-plane
coupling is increased. Quantum Monte Carlo results for the staggered structure
factor in combination with finite-size scaling theory give the critical ratio
between the inter-plane and in-plane coupling constants.
The critical behavior is consistent with the 3D classical Heisenberg
universality class. Results for the uniform magnetic susceptibility and the
correlation length at finite temperature are compared with recent predictions
for the 2+1-dimensional nonlinear -model. The susceptibility is found
to exhibit quantum critical behavior at temperatures significantly higher than
the correlation length.Comment: 11 pages (5 postscript figures available upon request), Revtex 3.
XXVI IUPAP Conference on Computational Physics (CCP2014)
The 26th IUPAP Conference on Computational Physics, CCP2014, was held in Boston, Massachusetts, during August 11-14, 2014. Almost 400 participants from 38 countries convened at the George Sherman Union at Boston University for four days of plenary and parallel sessions spanning a broad range of topics in computational physics and related areas.
The first meeting in the series that developed into the annual Conference on Computational Physics (CCP) was held in 1989, also on the campus of Boston University and chaired by our colleague Claudio Rebbi. The express purpose of that meeting was to discuss the progress, opportunities and challenges of common interest to physicists engaged in computational research. The conference having returned to the site of its inception, it is interesting to recect on the development of the field during the intervening years. Though 25 years is a short time for mankind, computational physics has taken giant leaps during these years, not only because of the enormous increases in computer power but especially because of the development of new methods and algorithms, and the growing awareness of the opportunities the new technologies and methods can offer. Computational physics now represents a ''third leg'' of research alongside analytical theory and experiments in almost all subfields of physics, and because of this there is also increasing specialization within the community of computational physicists. It is therefore a challenge to organize a meeting such as CCP, which must have suffcient depth in different areas to hold the interest of experts while at the same time being broad and accessible. Still, at a time when computational research continues to gain in importance, the CCP series is critical in the way it fosters cross-fertilization among fields, with many participants specifically attending in order to get exposure to new methods in fields outside their own.
As organizers and editors of these Proceedings, we are very pleased with the high quality of the papers provided by the participants. These articles represent a good cross-section of what was presented at the meeting, and it is our hope that they will not only be useful individually for their specific scientific content but will also represent a historical snapshot of the state of computational physics that they represent collectively.
The remainder of this Preface contains lists detailing the organizational structure of CCP2014, endorsers and sponsors of the meeting, plenary and invited talks, and a presentation of the 2014 IUPAP C20 Young Scientist Prize.
We would like to take the opportunity to again thank all those who contributed to the success of CCP214, as organizers, sponsors, presenters, exhibitors, and participants.
Anders Sandvik, David Campbell, David Coker, Ying TangPublished versio
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.
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.
Criticality in coupled quantum spin-chains with competing ladder-like and two-dimensional couplings
Motivated by the geometry of spins in the material CaCuO, we study a
two-layer, spin-half Heisenberg model, with nearest-neighbor exchange couplings
J and \alpha*J along the two axes in the plane and a coupling J_\perp
perpendicular to the planes. We study these class of models using the
Stochastic Series Expansion (SSE) Quantum Monte Carlo simulations at finite
temperatures and series expansion methods at T=0. The critical value of the
interlayer coupling, J_\perp^c, separating the N{\'e}el ordered and disordered
ground states, is found to follow very closely a square root dependence on
. Both T=0 and finite-temperature properties of the model are
presented.Comment: 9 pages, 11 figs., 1 tabl
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
Ground state of the random-bond spin-1 Heisenberg chain
Stochastic series expansion quantum Monte Carlo is used to study the ground
state of the antiferromagnetic spin-1 Heisenberg chain with bond disorder.
Typical spin- and string-correlations functions behave in accordance with
real-space renormalization group predictions for the random-singlet phase. The
average string-correlation function decays algebraically with an exponent of
-0.378(6), in very good agreement with the prediction of , while the average spin-correlation function is found to decay with an
exponent of about -1, quite different from the expected value of -2. By
implementing the concept of directed loops for the spin-1 chain we show that
autocorrelation times can be reduced by up to two orders of magnitude.Comment: 9 pages, 10 figure
Entanglement and Spontaneous Symmetry Breaking in Quantum Spin Models
It is shown that spontaneous symmetry breaking does not modify the
ground-state entanglement of two spins, as defined by the concurrence, in the
XXZ- and the transverse field Ising-chain. Correlation function inequalities,
valid in any dimensions for these models, are presented outlining the regimes
where entanglement is unaffected by spontaneous symmetry breaking
Various series expansions for the bilayer S=1/2 Heisenberg antiferromagnet
Various series expansions have been developed for the two-layer, S=1/2,
square lattice Heisenberg antiferromagnet. High temperature expansions are used
to calculate the temperature dependence of the susceptibility and specific
heat. At T=0, Ising expansions are used to study the properties of the
N\'{e}el-ordered phase, while dimer expansions are used to calculate the
ground-state properties and excitation spectra of the magnetically disordered
phase. The antiferromagnetic order-disorder transition point is determined to
be . Quantities computed include the staggered
magnetization, the susceptibility, the triplet spin-wave excitation spectra,
the spin-wave velocity, and the spin-wave stiffness. We also estimates that the
ratio of the intra- and inter-layer exchange constants to be for cuprate superconductor .Comment: RevTeX, 9 figure
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