210 research outputs found

### Low-Temperature Expansions and Correlation Functions of the Z_3-Chiral Potts Model

Using perturbative methods we derive new results for the spectrum and
correlation functions of the general Z_3-chiral Potts quantum chain in the
massive low-temperature phase. Explicit calculations of the ground state energy
and the first excitations in the zero momentum sector give excellent
approximations and confirm the general statement that the spectrum in the
low-temperature phase of general Z_n-spin quantum chains is identical to one in
the high-temperature phase where the role of charge and boundary conditions are
interchanged. Using a perturbative expansion of the ground state for the Z_3
model we are able to gain some insight in correlation functions. We argue that
they might be oscillating and give estimates for the oscillation length as well
as the correlation length.Comment: 17 pages (Plain TeX), BONN-HE-93-1

### Excitation Spectrum and Correlation Functions of the Z_3-Chiral Potts Quantum Spin Chain

We study the excitation spectrum and the correlation functions of the Z_3-
chiral Potts model in the massive high-temperature phase using perturbation
expansions and numerical diagonalization. We are mainly interested in results
for general chiral angles but we consider also the superintegrable case. For
the parameter values considered, we find that the band structure of the low-
lying part of the excitation spectrum has the form expected from a
quasiparticle picture with two fundamental particles. Studying the N-dependence
of the spectrum, we confirm the stability of the second fundamental particle in
a limited range of the momentum, even when its energy becomes so high that it
lies very high up among the multiparticle scattering states. This is not a
phenomenon restricted to the superintegrable line. Calculating a
non-translationally invariant correlation function, we give evidence that it is
oscillating. Within our numerical accuracy we find a relation between the
oscillation length and the dip position of the momentum dispersion of the
lightest particle which seems to be quite independent of the chiral angles.Comment: 19 pages + 6 PostScript figures (LaTeX); BONN-TH-94-2

### Onsager's algebra and partially orthogonal polynomials

The energy eigenvalues of the superintegrable chiral Potts model are
determined by the zeros of special polynomials which define finite
representations of Onsager's algebra. The polynomials determining the
low-sector eigenvalues have been given by Baxter in 1988. In the Z_3-case they
satisfy 4-term recursion relations and so cannot form orthogonal sequences.
However, we show that they are closely related to Jacobi polynomials and
satisfy a special "partial orthogonality" with respect to a Jacobi weight
function.Comment: 8 pages, no figure

### Identities in the Superintegrable Chiral Potts Model

We present proofs for a number of identities that are needed to study the
superintegrable chiral Potts model in the $Q\ne0$ sector.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 11 pages,
uses eufb10 and eurm10 fonts. Typeset twice! vs2: Two equations added. vs3:
Introduction adde

### Form factors of twist fields in the lattice Dirac theory

We study U(1) twist fields in a two-dimensional lattice theory of massive
Dirac fermions. Factorized formulas for finite-lattice form factors of these
fields are derived using elliptic parametrization of the spectral curve of the
model, elliptic determinant identities and theta functional interpolation. We
also investigate the thermodynamic and the infinite-volume scaling limit, where
the corresponding expressions reduce to form factors of the exponential fields
of the sine-Gordon model at the free-fermion point.Comment: 20 pages, 2 figure

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