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Yas-Hiro Quano

Publications and source records attributed to Yas-Hiro Quano.

17 recordsLinked to original sources
arXiv2015

Form factors of spin 1 analogue of the eight-vertex model

The twenty-one-vertex model, the spin $1$ analogue of the eight-vertex model is considered on the basis of free field representations of vertex operators in the $2\times 2$-fold fusion SOS model and vertex-face transformation. The tail operators, which translate corner transfer matrices of the twenty-one-vertex model into those of the fusion SOS model, are constructed by using free bosons and fermions for both diagonal and off-diagonal matrix elements with respect to the ground state sectors. Form factors of any local operators are therefore obtained in terms of multiple integral formulae, in principle. As the simplest example, the two-particle form factor of the spin operator is calculated explicitly.

math-ph↗
arXiv2011

A Vertex Operator Approach for Form Factors of Belavin's $(\mathbb{Z}/n\mathbb{Z})$-Symmetric Model and Its Application

A vertex operator approach for form factors of Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is constructed on the basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and vertex-face transformation. As simple application for $n=2$, we obtain expressions for $2m$-point form factors related to the $σ^z$ and $σ^x$ operators in the eight-vertex model.

math-ph↗
arXiv2010

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.

math-ph↗
arXiv2009

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.

math.QA↗
arXiv2004

Form factors, correlation functions and vertex operators in the eight-vertex model at reflectionless points

The eight-vertex model at the reflectionless points is considered on the basis of Smirnov's axiomatic approach. Integral formulae for form factors of the eight-vertex model can be obtained in terms of those of the eight-vertex SOS model, by using vertex-face transformation. The resulting formulae have very simple forms at the reflectionless points, and suggests us the explicit expressions of the type II vertex operators of the eight-vertex model.

hep-th↗
arXiv2002

Bootstrap equations and correlation functions for the Heisenberg XYZ antiferromagnet

Presented are two kinds of integral solutions to the quantum Knizhnik-Zamolodchikov equations for the 2n-point correlation functions of the Heisenberg XYZ antiferromagnet. Our first integral solution can be obtained from those for the cyclic SOS model by using the vertex-face correspondence. By the construction, the sum with respect to the local height variables k_0, k_1, >..., k_{2n} of the cyclic SOS model remains other than n-fold integral in the first solution. In order to perform those summations, we improve that to find the second integral solution of (r+1)n-fold integral for r in Z_{>1}, where r is a parameter of the XYZ model. Furthermore, we discuss the relations among our formula, Lashkevich-Pugai's formula and Shiraishi's one.

hep-th↗
arXiv2001

Smirnov-type integral formulae for correlation functions of the bulk/boundary XXZ model in the anti-ferromagnetic regime

Presented are the integral solutions to the quantum Knizhnik-Zamolodchikov equations for the correlation functions of both the bulk and boundary XXZ models in the anti-ferromagnetic regime. The difference equations can be derived from Smirnov-type master equations for correlation functions on the basis of the CTM bootstrap. Our integral solutions with an appropriate choice of the integral kernel reproduce the formulae previously obtained by using the bosonization of the vertex operators of the quantum affine algebra $U_q (\hat{\mathfrak{sl}_2})$.

hep-th↗
arXiv2001

Difference equations for correlation functions of $A^{(1)}_{n-1}$-face model with boundary reflection

The $A^{(1)}_{n-1}$-face model with boundary reflection is considered on the basis of the boundary CTM bootstrap. We construct the fused boundary Boltzmann weights to determine the normalization factor. We derive difference equations of the quantum Knizhnik-Zamolodchikov type for correlation functions of the boundary model. The simplest difference equations are solved the in the case of the free boundary condition.

hep-th↗
arXiv2000

Difference equations for correlation functions of Belavin's $Z_n$-symmetric model with boundary reflection

Belavin's $\mathbb{Z}_n$-symmetric elliptic model with boundary reflection is considered on the basis of the boundary CTM bootstrap. We find non-diagonal $K$-matrices for $n>2$ that satisfy the reflection equation (boundary Yang--Baxter equation), and also find non-diagonal Boltzmann weights for the $A^{(1)}_{n-1}$-face model even for $n\geqq 2$. We derive difference equations of the quantum Knizhnik-Zamolodchikov type for correlation functions of the boundary model. The boundary spontaneous polarization is obtained by solving the simplest difference equations. The resulting quantity is the square of the spontaneous polarization for the bulk $\mathbb{Z}_n$-symmetric model, up to a phase factor.

hep-th↗
arXiv1997

Form factors of the XXZ model and the affine quantum group symmetry

We present new expressions of form factors of the XXZ model which satisfy Smirnov's three axioms. These new form factors are obtained by acting the affine quantum group $U_q (\hat{\frak s \frak l_2})$ to the known ones obtained in our previous works. We also find the relations among all the new and known form factors, i.e., all other form factors can be expressed as kind of descendents of a special one.

hep-th↗
arXiv1994

Polynomial identities of the Rogers--Ramanujan type

Presented are polynomial identities which imply generalizations of Euler and Rogers--Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by establishing a graphical one-to-one correspondence between those two kinds of restricted partitions.

hep-th↗
arXiv1994

Virasoro character identities from the Andrews--Bailey construction

We prove $q$-series identities between bosonic and fermionic representations of certain Virasoro characters. These identities include some of the conjectures made by the Stony Brook group as special cases. Our method is a direct application of Andrews' extensions of Bailey's lemma to recently obtained polynomial identities.

hep-th↗
arXiv1994

On equivalence between Bose/Fermi Virasoro characters

On the basis of the Andrews--Bailey construction, we derive fermionic sum representations of Virasoro characters of non unitary minimal models ${\cal M}(k,kp+p-1)$ and ${\cal M}(k,kp+1)$. These expressions include certain expressions conjectured by the Stony Brook group as special cases.

hep-th↗
arXiv1993

Spontaneous Polarization of the $\Bbb Z _{n}$-Baxter Model

We show that correlation functions of the $\bz _n $-Baxter model in the principal regime satisfy a system of difference equations. We obtain the spontaneous polarization of the $\bz _n $-Baxter model as a solution of the simplest difference equation.

hep-th↗