455 research outputs found
Ginsparg-Wilson Relation and Ultralocality
It is shown that it is impossible to construct a free theory of fermions on
infinite hypercubic Euclidean lattice in four dimensions that is: (a)
ultralocal, (b) respects symmetries of hypercubic lattice, (c) corresponding
kernel satisfies D gamma5 + gamma5 D = D gamma5 D (Ginsparg-Wilson relation),
(d) describes single species of massless Dirac fermions in the continuum limit.Comment: 4 pages, REVTEX; few minor change
Towards Weyl fermions on the lattice without artefacts
In spite of the breakthrough in non-perturbative chiral gauge theories during
the last decade, the present formulation has stubborn artefacts. Independently
of the fermion representation one is confronted with unwanted CP violation and
infinitely many undetermined weight factors. Renormalization group identifies
the culprit. We demonstrate the procedure on Weyl fermions in a real
representation
Ginsparg-Wilson relation and the overlap formula
The fermionic determinant of a lattice Dirac operator that obeys the
Ginsparg-Wilson relation factorizes into two factors that are complex conjugate
of each other. Each factor is naturally associated with a single chiral fermion
and can be realized as a overlap of two many body vacua.Comment: 4 pages, plain tex, no figure
Solutions of the Ginsparg-Wilson Relation
We analyze general solutions of the Ginsparg-Wilson relation for lattice
Dirac operators and formulate a necessary condition for such operators to have
non-zero index in the topologically nontrivial background gauge fields.Comment: 6 pages, latex, no figures, set T to 1 in eqs. (10)--(13
Ginsparg-Wilson-Luscher Symmetry and Ultralocality
Important recent discoveries suggest that Ginsparg-Wilson-Luscher (GWL)
symmetry has analogous dynamical consequences for the theory on the lattice as
chiral symmetry does in the continuum. While it is well known that inherent
property of lattice chiral symmetry is fermion doubling, we show here that
inherent property of GWL symmetry is that the infinitesimal symmetry
transformation couples fermionic degrees of freedom at arbitrarily large
lattice distances (non-ultralocality). The consequences of this result for
ultralocality of symmetric actions are discussed.Comment: 18 pages, LATEX. For clarity changed to infinitesimal
transformations, typos corrected, explicit hypothesis adde
The Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths
The correlation length of the square-lattice spin-1/2 Heisenberg
antiferromagnet is studied in the low-temperature (asymptotic-scaling) regime.
Our novel approach combines a very efficient loop cluster algorithm --
operating directly in the Euclidean time continuum -- with finite-size scaling.
This enables us to probe correlation lengths up to
lattice spacings -- more than three orders of magnitude larger than any
previous study. We resolve a conundrum concerning the applicability of
asymptotic-scaling formulae to experimentally- and numerically-determined
correlation lengths, and arrive at a very precise determination of the
low-energy observables. Our results have direct implications for the
zero-temperature behavior of spin-1/2 ladders.Comment: 12 pages, RevTeX, plus two Postscript figures. Some minor
modifications for final submission to Physical Review Letters. (accepted by
PRL
Microcanonical finite-size scaling in specific heat diverging 2nd order phase transitions
A Microcanonical Finite Site Ansatz in terms of quantities measurable in a
Finite Lattice allows to extend phenomenological renormalization (the so called
quotients method) to the microcanonical ensemble. The Ansatz is tested
numerically in two models where the canonical specific-heat diverges at
criticality, thus implying Fisher-renormalization of the critical exponents:
the 3D ferromagnetic Ising model and the 2D four-states Potts model (where
large logarithmic corrections are known to occur in the canonical ensemble). A
recently proposed microcanonical cluster method allows to simulate systems as
large as L=1024 (Potts) or L=128 (Ising). The quotients method provides
extremely accurate determinations of the anomalous dimension and of the
(Fisher-renormalized) thermal exponent. While in the Ising model the
numerical agreement with our theoretical expectations is impressive, in the
Potts case we need to carefully incorporate logarithmic corrections to the
microcanonical Ansatz in order to rationalize our data.Comment: 13 pages, 8 figure
Finite size and temperature effects in the AF Heisenberg model
The low temperature and large volume effects in the d=2+1 antiferromagnetic
quantum Heisenberg model are dominated by magnon excitations. The leading and
next-to-leading corrections are fully controlled by three physical constants,
the spin stiffness, the spin wave velocity and the staggered magnetization.
Among others, the free energy, the ground state energy, the low lying
excitations, staggered magnetization, staggered and uniform susceptibilities
are studied here. The special limits of very low temperature and infinite
volume are considered also.Comment: 44 pages, LATEX, no figure
Role of the -resonance in determining the convergence of chiral perturbation theory
The dimensionless parameter , where
is the pion decay constant and is the pion mass, is expected to control
the convergence of chiral perturbation theory applicable to QCD. Here we
demonstrate that a strongly coupled lattice gauge theory model with the same
symmetries as two-flavor QCD but with a much lighter -resonance is
different. Our model allows us to study efficiently the convergence of chiral
perturbation theory as a function of . We first confirm that the leading
low energy constants appearing in the chiral Lagrangian are the same when
calculated from the -regime and the -regime as expected. However,
is necessary before 1-loop chiral perturbation theory
predicts the data within 1%. For the data begin to deviate
dramatically from 1-loop chiral perturbation theory predictions. We argue that
this qualitative change is due to the presence of a light -resonance in
our model. Our findings may be useful for lattice QCD studies.Comment: 5 pages, 6 figures, revtex forma
Simulations with different lattice Dirac operators for valence and sea quarks
We discuss simulations with different lattice Dirac operators for sea and
valence quarks. A goal of such a "mixed" action approach is to probe deeper the
chiral regime of QCD by enabling simulations with light valence quarks. This is
achieved by using chiral fermions as valence quarks while computationally
inexpensive fermions are used in the sea sector. Specifically, we consider
Wilson sea quarks and Ginsparg-Wilson valence quarks. The local Symanzik action
for this mixed theory is derived to O(a), and the appropriate low energy chiral
effective Lagrangian is constructed, including the leading O(a) contributions.
Using this Lagrangian one can calculate expressions for physical observables
and determine the Gasser-Leutwyler coefficients by fitting them to the lattice
data.Comment: 17 pages, 1 ps figure (2 clarification paragraphs added
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