24 research outputs found
EQSE Diagonalization of the Hubbard Model
The application of enhanced quasi-sparse eigenvector methods (EQSE) to the
Hubbard model is attempted. The ground state energy for the 4x4 Hubbard model
is calculated with a relatively small set of basis vectors. The results agree
to high precision with the exact answer. For the 8x8 case, exact answers are
not available but a simple first order correction to the quasi-sparse
eigenvector (QSE) result is presented.Comment: 5 pages, to appear in the proceedings of the International Light-Cone
Meeting on Non-Perturbative QCD and Hadron Phenomenology, Heidelberg, June
200
Renormalization in spherical field theory
We derive several results concerning non-perturbative renormalization in the
spherical field formalism. Using a small set of local counterterms, we are able
to remove all ultraviolet divergences in a manner such that the renormalized
theory is finite and translationally invariant. As an explicit example we
consider massless phi^4 theory in four dimensions.Comment: 16 pages, 5 figure
A Canonical Quantization of the Baker's Map
We present here a canonical quantization for the baker's map. The method we
use is quite different from that used in Balazs and Voros (ref.
\QCITE{cite}{}{BV}) and Saraceno (ref. \QCITE{cite}{}{S}). We first construct a
natural ``baker covering map'' on the plane \QTO{mathbb}{\mathbb{R}}^{2}. We
then use as the quantum algebra of observables the subalgebra of operators on
L^{2}(\QTO{mathbb}{\mathbb{R}}) generated by . We construct a unitary propagator such that
as the classical dynamics is returned. For Planck's constant
, we show that the dynamics can be reduced to the dynamics on an
-dimensional Hilbert space, and the unitary matrix propagator is
the same as given in ref. \QCITE{cite}{}{BV} except for a small correction of
order . This correction is shown to preserve the classical symmetry and in the quantum dynamics for periodic boundary conditions.Comment: 27 pages, 3 figures. Annals of Physics, to appea
The massless Thirring model in spherical field theory
We use the massless Thirring model to demonstrate a new approach to
non-perturbative fermion calculations based on the spherical field formalism.
The methods we present are free from the problems of fermion doubling and
difficulties associated with integrating out massless fermions. Using a
non-perturbative regularization, we compute the two-point correlator and find
agreement with the known analytic solution.Comment: 11 pages, 2 figures, journal versio
The diagonalization of quantum field Hamiltonians
We introduce a new diagonalization method called quasi-sparse eigenvector
diagonalization which finds the most important basis vectors of the low energy
eigenstates of a quantum Hamiltonian. It can operate using any basis, either
orthogonal or non-orthogonal, and any sparse Hamiltonian, either Hermitian,
non-Hermitian, finite-dimensional, or infinite-dimensional. The method is part
of a new computational approach which combines both diagonalization and Monte
Carlo techniques.Comment: 12 pages, 8 figures, new material adde
Modal expansions and non-perturbative quantum field theory in Minkowski space
We introduce a spectral approach to non-perturbative field theory within the
periodic field formalism. As an example we calculate the real and imaginary
parts of the propagator in 1+1 dimensional phi^4 theory, identifying both
one-particle and multi-particle contributions. We discuss the computational
limits of existing diagonalization algorithms and suggest new quasi-sparse
eigenvector methods to handle very large Fock spaces and higher dimensional
field theories.Comment: new material added, 12 pages, 6 figure
Spectrum and thermodynamic properties of two-dimensional N=(1,1) super Yang-Mills theory with fundamental matter and a Chern-Simons term
We consider N=(1,1) super Yang-Mills theory in 1+1 dimensions with
fundamentals at large-N_c. A Chern-Simons term is included to give mass to the
adjoint partons. Using the spectrum of the theory, we calculate thermodynamic
properties of the system as a function of the temperature and the Yang-Mills
coupling. In the large-N_c limit there are two non-communicating sectors, the
glueball sector, which we presented previously, and the meson-like sector that
we present here. We find that the meson-like sector dominates the
thermodynamics. Like the glueball sector, the meson sector has a Hagedorn
temperature T_H, and we show that the Hagedorn temperature grows with the
coupling. We calculate the temperature and coupling dependence of the free
energy for temperatures below T_H. As expected, the free energy for weak
coupling and low temperature grows quadratically with the temperature. Also the
ratio of the free energies at strong coupling compared to weak coupling,
r_{s-w}, for low temperatures grows quadratically with T. In addition, our data
suggest that r_{s-w} tends to zero in the continuum limit at low temperatures.Comment: 34 p