5,405 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
Supersolids in confined fermions on one-dimensional optical lattices
Using quantum Monte Carlo simulations, we show that density-density and
pairing correlation functions of the one-dimensional attractive fermionic
Hubbard model in a harmonic confinement potential are characterized by the
anomalous dimension of a corresponding periodic system, and hence
display quantum critical behavior. The corresponding fluctuations render the
SU(2) symmetry breaking by the confining potential irrelevant, leading to
structure form factors for both correlation functions that scale with the same
exponent upon increasing the system size, thus giving rise to a
(quasi)supersolid.Comment: 4 pages, 5 figures, published versio
Time evolution of correlations in strongly interacting fermions after a quantum quench
Using the adaptive time-dependent density matrix renormalization group, we
study the time evolution of density correlations of interacting spinless
fermions on a one-dimensional lattice after a sudden change in the interaction
strength. Over a broad range of model parameters, the correlation function
exhibits a characteristic light-cone-like time evolution representative of a
ballistic transport of information. Such behavior is observed both when
quenching an insulator into the metallic region and also when quenching within
the insulating region. However, when a metallic state beyond the quantum
critical point is quenched deep into the insulating regime, no indication for
ballistic transport is observed. Instead, stable domain walls in the density
correlations emerge during the time evolution, consistent with the predictions
of the Kibble-Zurek mechanism.Comment: Published version; minor changes, references adde
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
Bond-ordered states and -wave pairing of spinless fermions on the honeycomb lattice
Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor
interactions are known to harbour a quantum critical point at half-filling,
with critical behaviour in the Gross-Neveu (chiral Ising) universality class.
The critical interaction strength separates a weak-coupling semimetallic regime
from a commensurate charge-density-wave phase. The phase diagram of this basic
model of correlated fermions on the honeycomb lattice beyond half-filling is,
however, less well established. Here, we perform an analysis of its many-body
instabilities using the functional renormalization group method with a basic
Fermi surface patching scheme, which allows us to treat instabilities in
competing channels on equal footing also away from half-filling. Between
half-filling and the van-Hove filling, the free Fermi surface is hole-like and
we again find a charge-density wave instability to be dominant at large
interactions. Moreover, its characteristics are those of the half-filled case.
Directly at the van-Hove filling the nesting property of the free Fermi surface
stabilizes a dimerized bond-order phase. At lower filling the free Fermi
surface becomes electron-like and a superconducting instability with -wave
symmetry is found to emerge from the interplay of intra-unitcell repulsion and
collective fluctuations in the proximity to the charge-density wave
instability. We estimate the extent of the various phases and extract the
corresponding order parameters from the effective low-energy Hamiltonians.Comment: 11 pages, 11 figure
Z2 topological invariants in two dimensions from quantum Monte Carlo
We employ quantum Monte Carlo techniques to calculate the topological
invariant in a two-dimensional model of interacting electrons that exhibits a
quantum spin Hall topological insulator phase. In particular, we consider the
parity invariant for inversion-symmetric systems, which can be obtained from
the bulk's imaginary-time Green's function after an appropriate continuation to
zero frequency. This topological invariant is used here in order to study the
trivial-band to topological-insulator transitions in an interacting system with
spin-orbit coupling and an explicit bond dimerization. We discuss the
accessibility and behavior of this topological invariant within quantum Monte
Carlo simulations.Comment: 7 pages, 6 figure
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