Difference equations in spin chains with a boundary

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

Research output: Contribution to journalArticlepeer-review


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
Issue number3
StatePublished - Aug 21 1995
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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