Jordan cells of periodic loop models

Alexi Morin-Duchesne, Yvan Saint-Aubin

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


Jordan cells in transfer matrices of finite lattice models are a signature of the logarithmic character of the conformal field theories that appear in their thermodynamical limit. The transfer matrix of periodic loop models, T N, is an element of the periodic Temperley-Lieb algebra , where N is the number of sites on a section of the cylinder, and β = -q - q -1 = 2cos λ and the weights of contractible and non-contractible loops. The thermodynamic limit of TN is believed to describe a conformal field theory of central charge c = 1 - 6λ 2/(π(λ - π)). The abstract element TN acts naturally on (a sum of) spaces , similar to those upon which the standard modules of the (classical) Temperley-Lieb algebra act. These spaces known as sectors are labeled by the numbers of defects d and depend on a twist parameter v that keeps track of the winding of defects around the cylinder. Criteria are given for non-trivial Jordan cells of TN both between sectors with distinct defect numbers and within a given sector.

Original languageEnglish
Article number494013
JournalJournal of Physics A: Mathematical and Theoretical
Issue number49
Publication statusPublished - 13 Dec 2013
Externally publishedYes


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