329 research outputs found
Perfect Lattice Topology: The Quantum Rotor as a Test Case
Lattice actions and topological charges that are classically and quantum
mechanically perfect (i.e. free of lattice artifacts) are constructed
analytically for the quantum rotor. It is demonstrated that the Manton action
is classically perfect while the Villain action is quantum perfect. The
geometric construction for the topological charge is only perfect at the
classical level. The quantum perfect lattice topology associates a topological
charge distribution, not just a single charge, with each lattice field
configuration. For the quantum rotor with the classically perfect action and
topological charge, the remaining cut-off effects are exponentially suppressed.Comment: 12 pages, including two figures. ordinary LaTeX, requires fps.sty;
Submitted to Phys. Lett.
Quenched divergences in the deconfined phase of SU(2) gauge theory
The spectrum of the overlap Dirac operator in the deconfined phase of
quenched gauge theory is known to have three parts: exact zeros arising from
topology, small nonzero eigenvalues that result in a non-zero chiral
condensate, and the dense bulk of the spectrum, which is separated from the
small eigenvalues by a gap. In this paper, we focus on the small nonzero
eigenvalues in an SU(2) gauge field background at and . This
low-lying spectrum is computed on four different spatial lattices (,
, , and ). As the volume increases, the small eigenvalues
become increasingly concentrated near zero in such a way as to strongly suggest
that the infinite volume condensate diverges.Comment: 12 pages, 3 figures, version to appear in Physical Review
Boundary Limitation of Wavenumbers in Taylor-Vortex Flow
We report experimental results for a boundary-mediated wavenumber-adjustment
mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow
(TVF). The system consists of fluid contained between two concentric cylinders
with the inner one rotating at an angular frequency . As observed
previously, the Eckhaus instability (a bulk instability) is observed and limits
the stable wavenumber band when the system is terminated axially by two rigid,
non-rotating plates. The band width is then of order at small
() and agrees well with
calculations based on the equations of motion over a wide -range.
When the cylinder axis is vertical and the upper liquid surface is free (i.e.
an air-liquid interface), vortices can be generated or expelled at the free
surface because there the phase of the structure is only weakly pinned. The
band of wavenumbers over which Taylor-vortex flow exists is then more narrow
than the stable band limited by the Eckhaus instability. At small
the boundary-mediated band-width is linear in . These results are
qualitatively consistent with theoretical predictions, but to our knowledge a
quantitative calculation for TVF with a free surface does not exist.Comment: 8 pages incl. 9 eps figures bitmap version of Fig
Light Hadron Spectrum in Quenched Lattice QCD with Staggered Quarks
Without chiral extrapolation, we achieved a realistic nucleon to (\rho)-meson
mass ratio of (m_N/m_\rho = 1.23 \pm 0.04 ({\rm statistical}) \pm 0.02 ({\rm
systematic})) in our quenched lattice QCD numerical calculation with staggered
quarks. The systematic error is mostly from finite-volume effect and the
finite-spacing effect is negligible. The flavor symmetry breaking in the pion
and (\rho) meson is no longer visible. The lattice cutoff is set at 3.63 (\pm)
0.06 GeV, the spatial lattice volume is (2.59 (\pm) 0.05 fm)(^3), and bare
quarks mass as low as 4.5 MeV are used. Possible quenched chiral effects in
hadron mass are discussed.Comment: 5 pages and 5 figures, use revtex
Topological Lattice Actions
We consider lattice field theories with topological actions, which are
invariant against small deformations of the fields. Some of these actions have
infinite barriers separating different topological sectors. Topological actions
do not have the correct classical continuum limit and they cannot be treated
using perturbation theory, but they still yield the correct quantum continuum
limit. To show this, we present analytic studies of the 1-d O(2) and O(3)
model, as well as Monte Carlo simulations of the 2-d O(3) model using
topological lattice actions. Some topological actions obey and others violate a
lattice Schwarz inequality between the action and the topological charge Q.
Irrespective of this, in the 2-d O(3) model the topological susceptibility
\chi_t = \l/V is logarithmically divergent in the continuum limit.
Still, at non-zero distance the correlator of the topological charge density
has a finite continuum limit which is consistent with analytic predictions. Our
study shows explicitly that some classically important features of an action
are irrelevant for reaching the correct quantum continuum limit.Comment: 38 pages, 12 figure
Order a improved renormalization constants
We present non-perturbative results for the constants needed for on-shell
improvement of bilinear operators composed of Wilson fermions. We work
at and 6.2 in the quenched approximation. The calculation is done
by imposing axial and vector Ward identities on correlators similar to those
used in standard hadron mass calculations. A crucial feature of the calculation
is the use of non-degenerate quarks. We also obtain results for the constants
needed for off-shell improvement of bilinears, and for the scale and
scheme independent renormalization constants, (Z_A), (Z_V) and (Z_S/Z_P).
Several of the constants are determined using a variety of different Ward
identities, and we compare their relative efficacies. In this way, we find a
method for calculating that gives smaller errors than that used
previously. Wherever possible, we compare our results with those of the ALPHA
collaboration (who use the Schr\"odinger functional) and with 1-loop
tadpole-improved perturbation theory.Comment: 48 pages. Modified "axis" source for figures also included. Typos
corrected (version published in Phys. Rev. D
Vacuum structure of CP^N sigma models at theta=pi
We show that parity symmetry is not spontaneously broken in the CP^N sigma
model for any value of N when the coefficient of the --term becomes
(mod ). The result follows from a non-perturbative analysis
of the nodal structure of the vacuum functional . The dynamical role
of sphalerons turns out to be very important for the argument. The result
introduces severe constraints on the possible critical behavior of the models
at (mod ).Comment: 8 pages, revtex, to appear in Phys. Rev. Let
The Schwinger Model with Perfect Staggered Fermions
We construct and test a quasi-perfect lattice action for staggered fermions.
The construction starts from free fermions, where we suggest a new blocking
scheme, which leads to excellent locality of the perfect action. An adequate
truncation preserves a high quality of the free action. An Abelian gauge field
is inserted in d=2 by effectively tuning the couplings to a few short-ranged
lattice paths, based on the behavior of topological zero modes. We simulate the
Schwinger model with this action, applying a new variant of Hybrid Monte Carlo,
which damps the computational overhead due to the non-standard couplings. We
obtain a tiny ``pion'' mass down to very small \beta, while the ``\eta'' mass
follows very closely the prediction of asymptotic scaling. The observation that
even short-ranged quasi-perfect actions can yield strong improvement is most
relevant in view of QCD.Comment: 30 pages, 16 figures. Following the referee's suggestions, we have
incorporated the material of hep-lat/9803018 in this comprehensive pape
Light Hadron Spectrum and Quark Masses from Quenched Lattice QCD
We present details of simulations for the light hadron spectrum in quenched
QCD carried out on the CP-PACS parallel computer. Simulations are made with the
Wilson quark action and the plaquette gauge action on 32^3x56 - 64^3x112
lattices at four lattice spacings (a \approx 0.1-0.05 fm) and the spatial
extent of 3 fm. Hadronic observables are calculated at five quark masses
(m_{PS}/m_V \approx 0.75 - 0.4), assuming the u and d quarks being degenerate
but treating the s quark separately. We find that the presence of quenched
chiral singularities is supported from an analysis of the pseudoscalar meson
data. We take m_\pi, m_\rho and m_K (or m_\phi) as input. After chiral and
continuum extrapolations, the agreement of the calculated mass spectrum with
experiment is at a 10% level. In comparison with the statistical accuracy of
1-3% and systematic errors of at most 1.7% we have achieved, this demonstrates
a failure of the quenched approximation for the hadron spectrum: the meson
hyperfine splitting is too small, and the octet masses and the decuplet mass
splittings are both smaller than experiment. Light quark masses are calculated
using two definitions: the conventional one and the one based on the
axial-vector Ward identity. The two results converge toward the continuum
limit, yielding m_{ud}=4.29(14)^{+0.51}_{-0.79} MeV. The s quark mass depends
on the strange hadron mass chosen for input: m_s = 113.8(2.3)^{+5.8}_{-2.9} MeV
from m_K and m_s = 142.3(5.8)^{+22.0}_{-0} MeV from m_\phi, indicating again a
failure of the quenched approximation. We obtain \Lambda_{\bar{MS}}^{(0)}=
219.5(5.4) MeV. An O(10%) deviation from experiment is observed in the
pseudoscalar meson decay constants.Comment: 60 pages, 49 figure
Flavor Singlet Meson Mass in the Continuum Limit in Two-Flavor Lattice QCD
We present results for the mass of the eta-prime meson in the continuum limit
for two-flavor lattice QCD, calculated on the CP-PACS computer, using a
renormalization-group improved gauge action, and Sheikholeslami and Wohlert's
fermion action with tadpole-improved csw. Correlation functions are measured at
three values of the coupling constant beta corresponding to the lattice spacing
a approx. 0.22, 0.16, 0.11 fm and for four values of the quark mass parameter
kappa corresponding to mpi over mrho approx. 0.8, 0.75, 0.7 and 0.6. For each
beta, kappa pair, 400-800 gauge configurations are used. The two-loop diagrams
are evaluated using a noisy source method. We calculate eta-prime propagators
using local sources, and find that excited state contributions are much reduced
by smearing. A full analysis for the smeared propagators gives
metaprime=0.960(87)+0.036-0.248 GeV, in the continuum limit, where the second
error represents the systematic uncertainty coming from varying the functional
form for chiral and continuum extrapolations.Comment: 9 pages, 19 figures, 4 table
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