Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation

Daniel Arnaudon, Nicolas Crampé, Anastasia Doikou, Luc Frappat, Eric Ragoucy

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a generic gl(n)-spin chain possessing on each site an arbitrary gl(n)-representation. For open spin chains, we use the classification of the reflection matrices to treat all the diagonal boundary cases. As a result, we obtain the Bethe equations in their full generality for closed and open spin chains. The classifications of finite dimensional irreducible representations for the Yangian (closed spin chains) and for the reflection algebras (open spin chains) are directly linked to the calculation of the transfer matrix eigenvalues. As examples, we recover the usual closed and open spin chains, we treat the alternating spin chains and the closed spin chain with impurity.
Original languageEnglish
Article numberP02007
JournalJournal of Statistical Mechanics: Theory and Experiment
Publication statusPublished - Feb 2005


  • math-ph
  • cond-mat.str-el
  • math.MP
  • math.QA


Dive into the research topics of 'Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation'. Together they form a unique fingerprint.

Cite this