19 research outputs found

### Vertex operator approach for correlation functions of Belavin's (Z/nZ)-symmetric model

Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is considered on the
basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and
vertex-face transformation. The corner transfer matrix (CTM) Hamiltonian of
$(\mathbb{Z}/n\mathbb{Z})$-symmetric model and tail operators are expressed in
terms of bosonized vertex operators in the $A^{(1)}_{n-1}$ model. Correlation
functions of $(\mathbb{Z}/n\mathbb{Z})$-symmetric model can be obtained by
using these objects, in principle. In particular, we calculate spontaneous
polarization, which reproduces the result by myselves in 1993.Comment: For the next thirty days the full text of this article is available
at http://stacks.iop.org/1751-8121/42/16521

### Vertex operator approach for form factors of Belavin's $(Z/nZ)$-symmetric model

Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is considered on the
basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and
vertex-face transformation. Free field representations of nonlocal tail
operators are constructed for off diagonal matrix elements with respect to the
ground state sectors. As a result, integral formulae for form factors of any
local operators in the $(\mathbb{Z}/n\mathbb{Z})$-symmetric model can be
obtained, in principle.Comment: 24 pages, 4 figures, published in J. Phys. A: Math. Theor. 43 (2010)
085202. For the next thirty days from Feb 5 2010, the full text of the
article will be completely free to access through our 'This Month's Papers'
service (www.iop.org/journals/thismonth), helping you to benefit from maximum
visibilit

### Type II vertex operators for the $A_{n-1}^{(1)}$ face model

Presented is a free boson representation of the type II vertex operators for
the $A_{n-1}^{(1)}$ face model. Using the bosonization, we derive some
properties of the type II vertex operators, such as commutation, inversion and
duality relations.Comment: 20 pages, LaTEX 2

### The Vertex-Face Correspondence and the Elliptic 6j-symbols

A new formula connecting the elliptic $6j$-symbols and the fusion of the
vertex-face intertwining vectors is given. This is based on the identification
of the $k$ fusion intertwining vectors with the change of base matrix elements
from Sklyanin's standard base to Rosengren's natural base in the space of even
theta functions of order $2k$. The new formula allows us to derive various
properties of the elliptic $6j$-symbols, such as the addition formula, the
biorthogonality property, the fusion formula and the Yang-Baxter relation. We
also discuss a connection with the Sklyanin algebra based on the factorised
formula for the $L$-operator.Comment: 23 page

### Vertex--IRF correspondence and factorized L-operators for an elliptic R-operator

As for an elliptic $R$-operator which satisfies the Yang--Baxter equation,
the incoming and outgoing intertwining vectors are constructed, and the
vertex--IRF correspondence for the elliptic $R$-operator is obtained. The
vertex--IRF correspondence implies that the Boltzmann weights of the IRF model
satisfy the star--triangle relation. By means of these intertwining vectors,
the factorized L-operators for the elliptic $R$-operator are also constructed.
The vertex--IRF correspondence and the factorized L-operators for Belavin's
$R$-matrix are reproduced from those of the elliptic $R$-operator.Comment: 25 pages, amslatex, no figure

### Solution of the dual reflection equation for $A^{(1)}_{n-1}$ SOS model

We obtain a diagonal solution of the dual reflection equation for elliptic
$A^{(1)}_{n-1}$ SOS model. The isomorphism between the solutions of the
reflection equation and its dual is studied.Comment: Latex file 12 pages, added reference

### Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet

We exactly evaluate the third neighbor correlator and all
the possible non-zero correlators <S^{alpha}_j S^{beta}_{j+1} S^{gamma}_{j+2}
S^{delta}_{j+3}> of the spin-1/2 Heisenberg $XXX$ antiferromagnet in the ground
state without magnetic field. All the correlators are expressed in terms of
certain combinations of logarithm ln2, the Riemann zeta function zeta(3),
zeta(5) with rational coefficients. The results accurately coincide with the
numerical ones obtained by the density-matrix renormalization group method and
the numerical diagonalization.Comment: 4 page

### R-matrix Quantization of the Elliptic Ruijsenaars--Schneider model

It is shown that the classical L-operator algebra of the elliptic
Ruijsenaars-Schneider model can be realized as a subalgebra of the algebra of
functions on the cotangent bundle over the centrally extended current group in
two dimensions. It is governed by two dynamical r and $\bar{r}$-matrices
satisfying a closed system of equations. The corresponding quantum R and
$\overline{R}$-matrices are found as solutions to quantum analogs of these
equations. We present the quantum L-operator algebra and show that the system
of equations on R and $\overline{R}$ arises as the compatibility condition for
this algebra. It turns out that the R-matrix is twist-equivalent to the Felder
elliptic R^F-matrix with $\overline{R}$ playing the role of the twist. The
simplest representation of the quantum L-operator algebra corresponding to the
elliptic Ruijsenaars-Schneider model is obtained. The connection of the quantum
L-operator algebra to the fundamental relation RLL=LLR with Belavin's elliptic
R matrix is established. As a byproduct of our construction, we find a new
N-parameter elliptic solution to the classical Yang-Baxter equation.Comment: latex, 29 pages, some misprints are corrected and the meromorphic
version of the quantum L-operator algebra is discusse