Difference equations in spin chains with a boundary

Michio Jimbo, Rinat Kedem, Hitoshi Konno, Tetsuji Miwa, Robert Weston

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)429-456
Number of pages28
JournalNuclear Physics, Section B
Volume448
Issue number3
DOIs
StatePublished - Aug 21 1995
Externally publishedYes

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difference equations
apexes
form factors
axioms
boundary conditions
operators
magnetization
vacuum
matrices

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

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

In: Nuclear Physics, Section B, Vol. 448, No. 3, 21.08.1995, p. 429-456.

Research output: Contribution to journalArticle

Jimbo, Michio ; Kedem, Rinat ; Konno, Hitoshi ; Miwa, Tetsuji ; Weston, Robert. / Difference equations in spin chains with a boundary. In: Nuclear Physics, Section B. 1995 ; Vol. 448, No. 3. pp. 429-456.
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