TY - JOUR

T1 - Difference equations in spin chains with a boundary

AU - Jimbo, Michio

AU - Kedem, Rinat

AU - Konno, Hitoshi

AU - Miwa, Tetsuji

AU - Weston, Robert

N1 - Funding Information:
We wish to thank D. Bernard, E Fendley, T. Inami and A. Ludwig for useful discussions. R.A.W would like to thank P. Dorey for initially suggesting the CTM approach to boundary problems, and his colleagues at RIMS for their hospitality during the period in which much of this work was carried out. This work is partly supported by a Grant-in-Aid for Scientific Research on Priority Areas 231, the Ministry of Education, Science and Culture. H.K. is supported by Soryushi Shyogakukai. R.K. is supported by the Japan Society for the Promotion of Science.

PY - 1995/8/21

Y1 - 1995/8/21

N2 - 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-Zamolodchikov's result. The axioms satisfied by the form factors in the boundary theory are formulated.

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

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U2 - 10.1016/0550-3213(95)00218-H

DO - 10.1016/0550-3213(95)00218-H

M3 - Article

AN - SCOPUS:0346411612

SN - 0550-3213

VL - 448

SP - 429

EP - 456

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

ER -