Yang-Baxter equation in long-range interacting systems

D. Bernard, M. Gaudin, F. D.M. Haldane, V. Pasquier

Research output: Contribution to journalArticlepeer-review

231 Scopus citations


We consider the su(p) spin chains with long-range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying the Yang-Baxter equation. We obtain the expression of the conserved quantities of the dynamical models and we diagonalise them. In the spin chain case, we establish the connection between the degeneracies of the spectrum and the representation theory of the Yangians. We use a correspondence with the dynamical models to diagonalise the Hamiltonian. Finally, we extend the previous results to the case of a trigonometric R-matrix.

Original languageEnglish (US)
Article number010
Pages (from-to)5219-5236
Number of pages18
JournalJournal of Physics A: General Physics
Issue number20
StatePublished - 1993
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Mathematical Physics


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