Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain

P. Di Francesco, P. Zinn-Justin, J. B. Zuber

Research output: Contribution to journalArticlepeer-review

Abstract

The sums of components of the ground states of the O(1) loop model on a cylinder or of the XXZ quantum spin chain at Δ = -1/2 of size L are expressed in terms of combinatorial numbers. The methods include the introduction of spectral parameters and the use of integrability, a mapping from size L to L+1, and knot-theoretic skein relations.

Original languageEnglish (US)
Article numberP08011
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number8
DOIs
StatePublished - Aug 1 2006
Externally publishedYes

Keywords

  • Integrable spin chains (vertex models)
  • Loop models and polymers
  • Quantum integrability (Bethe ansatz)

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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