1,192 research outputs found
Spontaneous violation of CP symmetry in the strong interactions
Some time ago Dashen pointed out that spontaneous CP violation can occur in
the strong interactions. I show how a simple effective Lagrangian exposes the
remarkably large domain of quark mass parameters for which this occurs. I close
with some warnings for lattice simulations.Comment: 10 pages, 1 figure; final version to appear in PR
Low temperature expansion for the 3-d Ising Model
We compute the weak coupling expansion for the energy of the three
dimensional Ising model through 48 excited bonds. We also compute the
magnetization through 40 excited bonds. This was achieved via a recursive
enumeration of states of fixed energy on a set of finite lattices. We use a
linear combination of lattices with a generalization of helical boundary
conditions to eliminate finite volume effects.Comment: 10 pages, IASSNS-HEP-92/42, BNL-4767
Lattice QCD-2+1
We consider a 2+1-dimensional SU(N) lattice gauge theory in an axial gauge
with the link field U in the 1-direction set to one. The term in the
Hamiltonian containing the square of the electric field in the 1-direction is
non-local. Despite this non-locality, we show that weak-coupling perturbation
theory in this term gives a finite vacuum-energy density to second order, and
suggest that this property holds to all orders. Heavy quarks are confined, the
spectrum is gapped, and the space-like Wilson loop has area decay.Comment: Still Latex, 18 pages, no figures, with some further typographical
errors corrected. Version to appear in Phys. Rev.
Positivity and topology in lattice gauge theory
The admissibility condition usually used to define the topological charge in
lattice gauge theory is incompatible with a positive transfer matrix.Comment: 6 pages, revtex; revision has some clarifications and additional
references, representing the final version to appear in Physical Revie
An algorithm for simulating the Ising model on a type-II quantum computer
Presented here is an algorithm for a type-II quantum computer which simulates
the Ising model in one and two dimensions. It is equivalent to the Metropolis
Monte-Carlo method and takes advantage of quantum superposition for random
number generation. This algorithm does not require the ensemble of states to be
measured at the end of each iteration, as is required for other type-II
algorithms. Only the binary result is measured at each node which means this
algorithm could be implemented using a range of different quantum computing
architectures. The Ising model provides an example of how cellular automata
rules can be formulated to be run on a type-II quantum computer.Comment: 14 pages, 11 figures. Accepted for publication in Computer Physics
Communication
Spontaneous Breaking of Flavor Symmetry and Parity in the Nambu-Jona-Lasinio Model with Wilson Fermions
We study the lattice \njl~model with two flavors of Wilson fermions in the
large limit, where is the number of `colors'. For large values of the
four-fermion coupling we find a phase in which both, flavor symmetry and
parity, are spontaneously broken. In accordance with general expectations there
are three massless pions on the phase boundary, but only two of them remain
massless inside the broken phase. This is analogous to earlier results obtained
in lattice QCD, indicating that this behavior is a very general feature of the
Wilson term.Comment: 7 pages, 4 figures, LATEX, tared and uuencode
Theory of Abelian Projection
Analytic methods for Abelian projection are developed. A number of results
are obtained related to string tension measurements. It is proven that even
without gauge fixing, abelian projection yields string tensions of the
underlying non-Abelian theory. Strong arguments are given for similar results
in the case where gauge fixing is employed. The methods used emphasize that the
projected theory is derived from the underlying non-Abelian theory rather than
vice versa. In general, the choice of subgroup used for projection is not very
important, and need not be Abelian. While gauge fixing is shown to be in
principle unnecessary for the success of Abelian projection, it is
computationally advantageous for the same reasons that improved operators,
e.g., the use of fat links, are advantageous in Wilson loop measurements. Two
other issues, Casimir scaling and the conflict between projection and critical
universality, are also discussed.Comment: Minor corrections, new section added, 14 pages, 3 figures, RevTe
Spatial search and the Dirac equation
We consider the problem of searching a d-dimensional lattice of N sites for a
single marked location. We present a Hamiltonian that solves this problem in
time of order sqrt(N) for d>2 and of order sqrt(N) log(N) in the critical
dimension d=2. This improves upon the performance of our previous quantum walk
search algorithm (which has a critical dimension of d=4), and matches the
performance of a corresponding discrete-time quantum walk algorithm. The
improvement uses a lattice version of the Dirac Hamiltonian, and thus requires
the introduction of spin (or coin) degrees of freedom.Comment: 5 pages, 1 figur
Disappearance of the Abrikosov vortex above the deconfining phase transition in SU(2) lattice gauge theory
We calculate the solenoidal magnetic monopole current and electric flux
distributions at finite temperature in the presence of a static quark antiquark
pair. The simulation was performed using SU(2) lattice gauge theory in the
maximal Abelian gauge. We find that the monopole current and electric flux
distributions are quite different below and above the finite temperature
deconfining phase transition point and agree with predictions of the
Ginzburg-Landau effective theory.Comment: 12 pages, Revtex Latex, 6 figures - ps files will be sent upon
reques
Staggered fermions, zero modes, and flavor-singlet mesons
We examine the taste structure of eigenvectors of the staggered-fermion Dirac
operator. We derive a set of conditions on the eigenvectors of modes with small
eigenvalues (near-zero modes), such that staggered fermions reproduce the 't
Hooft vertex in the continuum limit. We also show that, assuming these
conditions, the correlators of flavor-singlet mesons are free of contributions
singular in , where is the quark mass. This conclusion holds also when
a single flavor of sea quark is represented by the fourth root of the
staggered-fermion determinant. We then test numerically, using the HISQ action,
whether these conditions hold on realistic lattice gauge fields. We find that
the needed structure does indeed emerge.Comment: 24 pages, 21 figures, v2 clarifies a dependence and matches published
versio
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