Difference Equations in Spin Chains with a Boundary

Details Difference Equations in Spin Chains with a Boundary Difference Equations in Spin Chains with a Boundary

1995-02-10

arxiv.org/abs/hep-th/9502060v1

Nucl.Phys. B448 (1995) 429-456

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, LaTeX with amssymbols.sty, 7 uuencoded postscript figures

Scientific paper

10.1016/0550-3213(95)00218-H

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 8-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--Zamolodchikov's result. The axioms satisfied by the form factors in the boundary theory are formulated.

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