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

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 Delta=-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...

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Bibliographic Details
Published inJournal of statistical mechanics Vol. 2006; no. 8; p. P08011
Main Authors Francesco, P Di, Zinn-Justin, P, Zuber, J-B
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.08.2006
Subjects
Combinatorics
Condensed Matter
Mathematical Physics
Mathematics
Physics
Statistical Mechanics
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Summary: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 Delta=-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.
ISSN:1742-5468
1742-5468
DOI:10.1088/1742-5468/2006/08/P08011