### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 429-456 |

Number of pages | 28 |

Journal | Nuclear Physics, Section B |

Volume | 448 |

Issue number | 3 |

DOIs | |

State | Published - Aug 21 1995 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics, Section B*,

*448*(3), 429-456. https://doi.org/10.1016/0550-3213(95)00218-H

**Difference equations in spin chains with a boundary.** / Jimbo, Michio; Kedem, Rinat; Konno, Hitoshi; Miwa, Tetsuji; Weston, Robert.

Research output: Contribution to journal › Article

*Nuclear Physics, Section B*, vol. 448, no. 3, pp. 429-456. https://doi.org/10.1016/0550-3213(95)00218-H

}

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

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.

UR - http://www.scopus.com/inward/record.url?scp=0346411612&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346411612&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:0346411612

VL - 448

SP - 429

EP - 456

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -