298 research outputs found
The Coupled Cluster Method in Hamiltonian Lattice Field Theory
The coupled cluster or exp S form of the eigenvalue problem for lattice
Hamiltonian QCD (without quarks) is investigated. A new construction
prescription is given for the calculation of the relevant coupled cluster
matrix elements with respect to an orthogonal and independent loop space basis.
The method avoids the explicit introduction of gauge group coupling
coefficients by mapping the eigenvalue problem onto a suitable set of character
functions, which allows a simplified procedure. Using appropriate group
theoretical methods, we show that it is possible to set up the eigenvalue
problem for eigenstates having arbitrary lattice momentum and lattice angular
momentum.Comment: LaTeX, no figur
Path Integral Monte Carlo Approach to the U(1) Lattice Gauge Theory in (2+1) Dimensions
Path Integral Monte Carlo simulations have been performed for U(1) lattice
gauge theory in (2+1) dimensions on anisotropic lattices. We extractthe static
quark potential, the string tension and the low-lying "glueball" spectrum.The
Euclidean string tension and mass gap decrease exponentially at weakcoupling in
excellent agreement with the predictions of Polyakov and G{\" o}pfert and Mack,
but their magnitudes are five times bigger than predicted. Extrapolations are
made to the extreme anisotropic or Hamiltonian limit, and comparisons are made
with previous estimates obtained in the Hamiltonian formulation.Comment: 12 pages, 16 figure
Hamiltonian Study of Improved Lattice Gauge Theory in Three Dimensions
A comprehensive analysis of the Symanzik improved anisotropic
three-dimensional U(1) lattice gauge theory in the Hamiltonian limit is made.
Monte Carlo techniques are used to obtain numerical results for the static
potential, ratio of the renormalized and bare anisotropies, the string tension,
lowest glueball masses and the mass ratio. Evidence that rotational symmetry is
established more accurately for the Symanzik improved anisotropic action is
presented. The discretization errors in the static potential and the
renormalization of the bare anisotropy are found to be only a few percent
compared to errors of about 20-25% for the unimproved gauge action. Evidence of
scaling in the string tension, antisymmetric mass gap and the mass ratio is
observed in the weak coupling region and the behaviour is tested against
analytic and numerical results obtained in various other Hamiltonian studies of
the theory. We find that more accurate determination of the scaling
coefficients of the string tension and the antisymmetric mass gap has been
achieved, and the agreement with various other Hamiltonian studies of the
theory is excellent. The improved action is found to give faster convergence to
the continuum limit. Very clear evidence is obtained that in the continuum
limit the glueball ratio approaches exactly 2, as expected in a
theory of free, massive bosons.Comment: 13 pages, 15 figures, submitted to Phys. Rev.
The Coupled Cluster Method in Hamiltonian Lattice Field Theory: SU(2) Glueballs
The glueball spectrum within the Hamiltonian formulation of lattice gauge
theory (without fermions) is calculated for the gauge group SU(2) and for two
spatial dimensions.
The Hilbert space of gauge-invariant functions of the gauge field is
generated by its parallel-transporters on closed paths along the links of the
spatial lattice. The coupled cluster method is used to determine the spectrum
of the Kogut-Susskind Hamiltonian in a truncated basis. The quality of the
description is studied by computing results from various truncations, lattice
regularisations and with an improved Hamiltonian.
We find consistency for the mass ratio predictions within a scaling region
where we obtain good agreement with standard lattice Monte Carlo results.Comment: 13 pages, 7 figure
An Application of Feynman-Kleinert Approximants to the Massive Schwinger Model on a Lattice
A trial application of the method of Feynman-Kleinert approximants is made to
perturbation series arising in connection with the lattice Schwinger model. In
extrapolating the lattice strong-coupling series to the weak-coupling continuum
limit, the approximants do not converge well. In interpolating between the
continuum perturbation series at large fermion mass and small fermion mass,
however, the approximants do give good results. In the course of the
calculations, we picked up and rectified an error in an earlier derivation of
the continuum series coefficients.Comment: 16 pages, 4 figures, 5 table
Density Matrix Renormalisation Group Approach to the Massive Schwinger Model
The massive Schwinger model is studied, using a density matrix
renormalisation group approach to the staggered lattice Hamiltonian version of
the model. Lattice sizes up to 256 sites are calculated, and the estimates in
the continuum limit are almost two orders of magnitude more accurate than
previous calculations. Coleman's picture of `half-asymptotic' particles at
background field theta = pi is confirmed. The predicted phase transition at
finite fermion mass (m/g) is accurately located, and demonstrated to belong in
the 2D Ising universality class.Comment: 38 pages, 18 figures, submitted to PR
Finite-size correction and bulk hole-excitations for special case of an open XXZ chain with nondiagonal boundary terms at roots of unity
Using our solution for the open spin-1/2 XXZ quantum spin chain with N spins
and two arbitrary boundary parameters at roots of unity, the central charge and
the conformal dimensions for bulk hole excitations are derived from the 1/N
correction to the energy (Casimir energy).Comment: 21 pages, LaTeX, v2: minor changes and 3 references adde
A New Finite-lattice study of the Massive Schwinger Model
A new finite lattice calculation of the low lying bound state energies in the
massive Schwinger model is presented, using a Hamiltonian lattice formulation.
The results are compared with recent analytic series calculations in the low
mass limit, and with a new higher order non-relativistic series which we
calculate for the high mass limit. The results are generally in good agreement
with these series predictions, and also with recent calculations by light cone
and related techniques
Improved Lattice Gauge Field Hamiltonian
Lepage's improvement scheme is a recent major progress in lattice ,
allowing to obtain continuum physics on very coarse lattices. Here we discuss
improvement in the Hamiltonian formulation, and we derive an improved
Hamiltonian from a lattice Lagrangian free of errors. We do this by
the transfer matrix method, but we also show that the alternative via Legendre
transformation gives identical results. We consider classical improvement,
tadpole improvement and also the structure of L{\"u}scher-Weisz improvement.
The resulting color-electric energy is an infinite series, which is expected to
be rapidly convergent. For the purpose of practical calculations, we construct
a simpler improved Hamiltonian, which includes only nearest-neighbor
interactions.Comment: 30 pages, LaTe
The Hamiltonian limit of (3+1)D SU(3) lattice gauge theory on anisotropic lattices
The extreme anisotropic limit of Euclidean SU(3) lattice gauge theory is
examined to extract the Hamiltonian limit, using standard path integral Monte
Carlo (PIMC) methods. We examine the mean plaquette and string tension and
compare them to results obtained within the Hamiltonian framework of Kogut and
Susskind. The results are a significant improvement upon previous Hamiltonian
estimates, despite the extrapolation procedure necessary to extract
observables. We conclude that the PIMC method is a reliable method of obtaining
results for the Hamiltonian version of the theory. Our results also clearly
demonstrate the universality between the Hamiltonian and Euclidean formulations
of lattice gauge theory. It is particularly important to take into account the
renormalization of both the anisotropy, and the Euclidean coupling ,
in obtaining these results.Comment: 10 pages, 11 figure
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