Hitoshi Konno

XXZ chain with a boundary

The XXZ spin chain with a boundary magnetic field h is considered, using the vertex operator approach to diagonalize the hamiltonian. We find explicit bosonic formulas for the two vacuum vectors with zero particle content. There are three distinct regions when h ⩾ 0, in which the structure of the vacuum states is different. Excited states are given by the action of vertex operators on the vacuum states. We derive the boundary S-matrix and present an integral formula for the correlation functions. The boundary magnetization exhibits boundary hysteresis. We also discuss the rational limit, the XXX model.

Difference equations in spin chains with a boundary

Correlation functions and form factors in vertex models or spin chains are known to satisfy certain difference equations called the quantum Knizhnik-Zamolodchikov equations. We find similar difference equations for the case of semi-infinite spin chain systems with integrable boundary conditions. We derive these equations using the properties of the vertex operators and the boundary vacuum state, or alternatively through corner transfer matrix arguments for the eight-vertex model with a boundary. The spontaneous boundary magnetization is found by solving such difference equations. The boundary S-matrix is also proposed and compared, in the sine-Gordon limit, with Ghoshal-Zamolodchikovs result. The axioms satisfied by the form factors in the boundary theory are formulated.

Free-field representation of the quantum affine algebra Uq(sl2) and form factors in the higher-spin XXZ model

Abstract We consider the spin - 1 2 k XXZ model in the antiferromagnetic regime using the free-field realization of the quantum affine algebra U q ( sl 2 ) of level k . We give a free-field realization of the type-II q -vertex operator, which describes creation and annihilation of physical particles in the model. By taking a trace of the type-I and type-II q -vertex operators over the irreducible highest-weight representation of U q ( sl 2 ) , we also derive an integral formula for form factors in this model. Investigating the structure of poles, we obtain a residue formula for form factors, which is a lattice analog of the higher-spin extension of Smirnovs formula in the massive integrable quantum field theory. This result as well as the quantum deformation of the Knizhnik-Zamolodchikov equation for form factors shows a deep connection in the mathematical structure of the integrable lattice models and the massive integrable quantum field theory.

Relativistic Calogero - Sutherland model: spin generalization, quantum affine symmetry and dynamical correlation functions

Spin generalization of the relativistic Calogero - Sutherland model is constructed by using the affine Hecke algebra and shown to possess the quantum affine symmetry . The spinless model is exactly diagonalized by means of the Macdonald symmetric polynomials. The dynamical density - density correlation function, as well as the one-particle Green function, are evaluated exactly. We also investigate the finite-size scaling of the model and show that the low-energy behaviour is described by the C = 1 Gaussian theory with a new selection rule. The results indicate that the excitations obey the fractional exclusion statistics and also exhibit the Tomonaga - Luttinger liquid behaviour.

Dynamical correlation functions and finite-size scaling in the Ruij senaars-Schneider model

Abstract The trigonometric Ruijsenaars-Schneider model is diagonalized by means of the Macdonald symmetric functions. We evaluate the dynamical density-density correlation function and the one-particle retarded Green function as well as their thermodynamic limit. Based on these results and finite-size scaling analysis, we show that the low-energy behavior of the model is described by the C = 1 Gaussian conformal field theory under a new fractional selection rule for the quantum numbers labefing the critical exponents.

Free Field Representation of Level-k Yangian Double DY(sl2) k and deformation of Wakimoto Modules

A free field representation of level-k (≠0,–2) Yangian double DY(sl2)k and a corresponding deformation of Wakimoto modules are presented. We also realize two Types of vertex operators intertwining these modules.

Elliptic Quantum Group U_{q,p}(\hat{sl}_2) and Vertex Operators

Introducing an H-Hopf algebroid structure into U_{q,p}(\widedhat{sl}_2), we investigate the vertex operators of the elliptic quantum group U_{q,p}(\widedhat{sl}_2) defined as intertwining operators of infinite dimensional U_{q,p}(\widedhat{sl}_2)-modules. We show that the vertex operators coincide with the previous results obtained indirectly by using the quasi-Hopf algebra B_{q,\lambda}(\hat{sl}_2). This shows a consistency of our H-Hopf algebroid structure even in the case with non-zero central element.Introducing an H-Hopf algebroid structure into , we investigate the vertex operators of the elliptic quantum group defined as intertwining operators of infinite dimensional modules. We show that the vertex operators coincide with the previous results obtained indirectly by using the quasi-Hopf algebra . This shows a consistency of our H-Hopf algebroid structure even in the case with a nonzero central element.

An Elliptic Algebra

Abstract:We introduce an elliptic algebra with and present its free boson representation at generic level k. We show that this algebra governs a structure of the space of states in the k-fusion RSOS model specified by a pair of positive integers (r,k), or equivalently a q-deformation of the coset conformal field theory . Extending the work by Lukyanov and Pugai corresponding to the case k= 1, we give a full set of screening operators for k > 1. The algebra has two interesting degeneration limits, p→ 0 and p→ 1. The former limit yields the quantum affine algebra whereas the latter yields the algebra , the scaling limit of the elliptic algebra . Using this correspondence, we also obtain the highest component of two types of vertex operators which can be regarded as q-deformations of the primary fields in the coset conformal field theory.

U_{q,p}(\hat{sl_2})

Construction of integrable field theories in space with a boundary is extended to fermionic models. We obtain general forms of boundary interactions consistent with integrability of the massive Thirring model and study the duality equivalence of the MT model and the sine-Gordon model with boundary terms. We find a variety of integrable boundary interactions in the O(3) Gross-Neveu model from the boundary supersymmetric sine-Gordon theory by using boson-fermion duality.

and the Fusion RSOS Model

After reviewing the recent results on the Drinfeld realization of the face-type elliptic quantum group by the elliptic algebra , we investigate a fusion of the vertex operators of . The basic generating functions Λj(z)(1 ≤ j ≤ N − 1) of the deformed WN algebra are derived explicitly.After reviewing the recent results on the Drinfeld realization of the face type elliptic quantum group B_{q,lambda}(sl_N^) by the elliptic algebra U_{q,p}(sl_N^), we investigate a fusion of the vertex operators of U_{q,p}(sl_N^). The basic generating functions \Lambda_j(z) (j=1,2,.. N-1) of the deformed W_N algebra are derived explicitly.