4,574 research outputs found
Classical and quantum two-dimensional anisotropic Heisenberg antiferromagnets
The classical and the quantum, spin $S=1/2, versions of the uniaxially
anisotropic Heisenberg antiferromagnet on a square lattice in a field parallel
to the easy axis are studied using Monte Carlo techniques. For the classical
version, attention is drawn to biconical structures and fluctuations at low
temperatures in the transition region between the antiferromagnetic and
spin-flop phases. For the quantum version, the previously proposed scenario of
a first-order transition between the antiferromagnetic and spin-flop phases
with a critical endpoint and a tricritical point is scrutinized.Comment: 5 pages, 7 figures, accepted by Phys. Rev.
The Impact of Prior Assumptions on Bayesian Estimates of Inflation Parameters and the Expected Gravitational Waves Signal from Inflation
There has been much recent discussion, and some confusion, regarding the use
of existing observational data to estimate the likelihood that next-generation
cosmic microwave background (CMB) polarization experiments might detect a
nonzero tensor signal, possibly associated with inflation. We examine this
issue in detail here in two different ways: (1) first we explore the effect of
choice of different parameter priors on the estimation of the tensor-to-scalar
ratio r and other parameters describing inflation, and (2) we examine the
Bayesian complexity in order to determine how effectively existing data can
constrain inflationary parameters. We demonstrate that existing data are not
strong enough to render full inflationary parameter estimates in a
parametrization- and prior-independent way and that the predicted tensor signal
is particularly sensitive to different priors. For parametrizations where the
Bayesian complexity is comparable to the number of free parameters we find that
a flat prior on the scale of inflation (which is to be distinguished from a
flat prior on the tensor-to-scalar ratio) leads us to infer a larger, and in
fact slightly nonzero tensor contribution at 68% confidence level. However, no
detection is claimed. Our results demonstrate that all that is statistically
relevant at the current time is the (slightly enhanced) upper bound on r, and
we stress that the data remain consistent with r = 0.Comment: 9 pages, 5 figures. Section added on Bayesian complexity. Matches
published versio
Non-local updates for quantum Monte Carlo simulations
We review the development of update schemes for quantum lattice models
simulated using world line quantum Monte Carlo algorithms. Starting from the
Suzuki-Trotter mapping we discuss limitations of local update algorithms and
highlight the main developments beyond Metropolis-style local updates: the
development of cluster algorithms, their generalization to continuous time, the
worm and directed-loop algorithms and finally a generalization of the flat
histogram method of Wang and Landau to quantum systems.Comment: 14 pages, article for the proceedings of the "The Monte Carlo Method
in the Physical Sciences: Celebrating the 50th Anniversary of the Metropolis
Algorithm", Los Alamos, June 9-11, 200
Local density approximation for confined bosons in an optical lattice
We investigate local and global properties of the one-dimensional
Bose-Hubbard model with an external confining potential, describing an atomic
condensate in an optical lattice. Using quantum Monte Carlo techniques we
demonstrate that a local-density approximation, which relates the unconfined
and the confined model, yields quantitatively correct results in most of the
interesting parameter range. We also examine claims of universal behavior in
the confined system, and demonstrate the origin of a previously calculated fine
structure in the experimentally accessible momentum distribution.Comment: 7 pages, 11 figures; Section III updated and references adde
Ground state phase diagram of the half-filled bilayer Hubbard model
Employing a combination of functional renormalization group calculations and
projective determinantal quantum Monte Carlo simulations, we examine the
Hubbard model on the square lattice bilayer at half filling. From this combined
analysis, we obtain a comprehensive account on the ground state phase diagram
with respect to the extent of the system's metallic and (antiferromagnetically
ordered) Mott-insulating as well as band-insulating regions. By means of an
unbiased functional renormalization group approach, we exhibit the
antiferromagnetic Mott-insulating state as the relevant instability of the free
metallic state, induced by any weak finite onsite repulsion. Upon performing a
careful analysis of the quantum Monte Carlo data, we resolve the difficulty of
identifying this antiferromagnetic ground state for finite interlayer hopping
in the weak-coupling regime, where nonmonotonous finite-size corrections are
shown to relate to the two-sheeted Fermi surface structure of the metallic
phase. On the other hand, quantum Monte Carlo simulations are well suited to
identify the transition between the Mott-insulating phase and the band
insulator in the intermediate-to-strong coupling regime. Here, we compare our
numerical findings to indications for the transition region obtained from the
functional renormalization group procedure.Comment: 12 pages, 15 figure
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