536 research outputs found
Bethe Ansatz solutions for Temperley-Lieb Quantum Spin Chains
We solve the spectrum of quantum spin chains based on representations of the
Temperley-Lieb algebra associated with the quantum groups for and . The tool is a
modified version of the coordinate Bethe Ansatz through a suitable choice of
the Bethe states which give to all models the same status relative to their
diagonalization. All these models have equivalent spectra up to degeneracies
and the spectra of the lower dimensional representations are contained in the
higher-dimensional ones. Periodic boundary conditions, free boundary conditions
and closed non-local boundary conditions are considered. Periodic boundary
conditions, unlike free boundary conditions, break quantum group invariance.
For closed non-local cases the models are quantum group invariant as well as
periodic in a certain sense.Comment: 28 pages, plain LaTex, no figures, to appear in Int. J. Mod. Phys.
Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices
It has been shown in earlier works that for Q=0 and L a multiple of N, the
ground state sector eigenspace of the superintegrable tau_2(t_q) model is
highly degenerate and is generated by a quantum loop algebra L(sl_2).
Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2
algebras. For Q not equal 0, we shall show here that the corresponding
eigenspace of tau_2(t_q) is still highly degenerate, but splits into two
spaces, each containing 2^{r-1} independent eigenvectors. The generators for
the sl_2 subalgebras, and also for the quantum loop subalgebra, are given
generalizing those in the Q=0 case. However, the Serre relations for the
generators of the loop subalgebra are only proven for some states, tested on
small systems and conjectured otherwise. Assuming their validity we construct
the eigenvectors of the Q not equal 0 ground state sectors for the transfer
matrix of the superintegrable chiral Potts model.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 28 pages,
uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added,
improvements and minor corrections made, erratum to paper 2 included. Version
3: Small paragraph added in introductio
p-species integrable reaction-diffusion processes
We consider a process in which there are p-species of particles, i.e.
A_1,A_2,...,A_p, on an infinite one-dimensional lattice. Each particle
can diffuse to its right neighboring site with rate , if this site is not
already occupied. Also they have the exchange interaction A_j+A_i --> A_i+A_j
with rate We study the range of parameters (interactions) for which
the model is integrable. The wavefunctions of this multi--parameter family of
integrable models are found. We also extend the 2--species model to the case in
which the particles are able to diffuse to their right or left neighboring
sites.Comment: 16 pages, LaTe
The anisotropic XY model on the inhomogeneous periodic chain
The static and dynamic properties of the anisotropic XY-model on
the inhomogeneous periodic chain, composed of cells with different
exchange interactions and magnetic moments, in a transverse field are
determined exactly at arbitrary temperatures. The properties are obtained by
introducing the Jordan-Wigner fermionization and by reducing the problem to a
diagonalization of a finite matrix of order. The quantum transitions are
determined exactly by analyzing, as a function of the field, the induced
magnetization 1/n\sum_{m=1}^{n}\mu_{m}\left ( denotes
the cell, the site within the cell, the magnetic moment at site
within the cell) and the spontaneous magnetization which is obtained from the correlations for large spin separations. These results,
which are obtained for infinite chains, correspond to an extension of the ones
obtained by Tong and Zhong(\textit{Physica B} \textbf{304,}91 (2001)). The
dynamic correlations, , and the dynamic
susceptibility, are also obtained at arbitrary
temperatures. Explicit results are presented in the limit T=0, where the
critical behaviour occurs, for the static susceptibility as
a function of the transverse field , and for the frequency dependency of
dynamic susceptibility .Comment: 33 pages, 13 figures, 01 table. Revised version (minor corrections)
accepted for publiction in Phys. Rev.
Dynamic properties of the spin-1/2 XY chain with three-site interactions
We consider a spin-1/2 XY chain in a transverse (z) field with multi-site
interactions. The additional terms introduced into the Hamiltonian involve
products of spin components related to three adjacent sites. A Jordan-Wigner
transformation leads to a simple bilinear Fermi form for the resulting
Hamiltonian and hence the spin model admits a rigorous analysis. We point out
the close relationships between several variants of the model which were
discussed separately in previous studies. The ground-state phases (ferromagnet
and two kinds of spin liquid) of the model are reflected in the dynamic
structure factors of the spin chains, which are the main focus in this study.
First we consider the zz dynamic structure factor reporting for this quantity a
closed-form expression and analyzing the properties of the two-fermion
(particle-hole) excitation continuum which governs the dynamics of transverse
spin component fluctuations and of some other local operator fluctuations. Then
we examine the xx dynamic structure factor which is governed by many-fermion
excitations, reporting both analytical and numerical results. We discuss some
easily recognized features of the dynamic structure factors which are
signatures for the presence of the three-site interactions.Comment: 28 pages, 10 fugure
Eigenvectors in the Superintegrable Model I: sl_2 Generators
In order to calculate correlation functions of the chiral Potts model, one
only needs to study the eigenvectors of the superintegrable model. Here we
start this study by looking for eigenvectors of the transfer matrix of the
periodic tau_2(t)model which commutes with the chiral Potts transfer matrix. We
show that the degeneracy of the eigenspace of tau_2(t) in the Q=0 sector is
2^r, with r=(N-1)L/N when the size of the transfer matrix L is a multiple of N.
We introduce chiral Potts model operators, different from the more commonly
used generators of quantum group U-tilde_q(sl-hat(2)). From these we can form
the generators of a loop algebra L(sl(2)). For this algebra, we then use the
roots of the Drinfeld polynomial to give new explicit expressions for the
generators representing the loop algebra as the direct sum of r copies of the
simple algebra sl(2).Comment: LaTeX 2E document, 11 pages, 1 eps figure, using iopart.cls with
graphicx and iopams packages. v2: Appended text to title, added
acknowledgments and made several minor corrections v3: Added reference,
eliminated ambiguity, corrected a few misprint
The Onsager Algebra Symmetry of -matrices in the Superintegrable Chiral Potts Model
We demonstrate that the -matrices in the superintegrable chiral
Potts model possess the Onsager algebra symmetry for their degenerate
eigenvalues. The Fabricius-McCoy comparison of functional relations of the
eight-vertex model for roots of unity and the superintegrable chiral Potts
model has been carefully analyzed by identifying equivalent terms in the
corresponding equations, by which we extract the conjectured relation of
-operators and all fusion matrices in the eight-vertex model corresponding
to the -relation in the chiral Potts model.Comment: Latex 21 pages; Typos added, References update
Supersymmetric t-J Gaudin Models and KZ Equations
Supersymmetric t-J Gaudin models with both periodic and open boundary
conditions are constructed and diagonalized by means of the algebraic Bethe
ansatz method. Off-shell Bethe ansatz equations of the Gaudin systems are
derived, and used to construct and solve the KZ equations associated with
superalgebra.Comment: LaTex 21 page
Eigenvectors in the Superintegrable Model II: Ground State Sector
In 1993, Baxter gave eigenvalues of the transfer matrix of the
-state superintegrable chiral Potts model with spin-translation quantum
number , where . In our previous paper we
studied the Q=0 ground state sector, when the size of the transfer matrix
is chosen to be a multiple of . It was shown that the corresponding
matrix has a degenerate eigenspace generated by the generators of
simple algebras. These results enable us to express the transfer matrix
in the subspace in terms of these generators and for
. Moreover, the corresponding eigenvectors of the transfer
matrix are expressed in terms of rotated eigenvectors of .Comment: LaTeX 2E document, using iopart.cls with iopams packages. 17 pages,
uses eufb10 and eurm10 fonts. Typeset twice! vs2: Many changes and additions,
adding 7 pages. vs3: minor corrections. vs4 minor improvement
Integrability as a consequence of discrete holomorphicity: the Z_N model
It has recently been established that imposing the condition of discrete
holomorphicity on a lattice parafermionic observable leads to the critical
Boltzmann weights in a number of lattice models. Remarkably, the solutions of
these linear equations also solve the Yang-Baxter equations. We extend this
analysis for the Z_N model by explicitly considering the condition of discrete
holomorphicity on two and three adjacent rhombi. For two rhombi this leads to a
quadratic equation in the Boltzmann weights and for three rhombi a cubic
equation. The two-rhombus equation implies the inversion relations. The
star-triangle relation follows from the three-rhombus equation. We also show
that these weights are self-dual as a consequence of discrete holomorphicity.Comment: 11 pages, 7 figures, some clarifications and a reference adde
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