Jordan cells of periodic loop models

Morin-Duchesne, Alexi and Saint-Aubin, Yvan (2013) Jordan cells of periodic loop models. Journal of Physics A: Mathematical and Theoretical, 46 49: 494013.1-494013.47. doi:10.1088/1751-8113/46/49/494013


Author Morin-Duchesne, Alexi
Saint-Aubin, Yvan
Title Jordan cells of periodic loop models
Journal name Journal of Physics A: Mathematical and Theoretical   Check publisher's open access policy
ISSN 1751-8113
1751-8121
Publication date 2013-12
Year available 2013
Sub-type Article (original research)
DOI 10.1088/1751-8113/46/49/494013
Open Access Status DOI
Volume 46
Issue 49
Start page 494013.1
End page 494013.47
Total pages 47
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2014
Language eng
Formatted abstract
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.
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
 
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