Fusion hierarchies, T-systems, and Y-systems of logarithmic minimal models
Alexi Morin-Duchesne, Paul A Pearce, Jorgen Rasmussen
Journal of Statistical Mechanics Theory and Experiment | IOP PUBLISHING LTD | Published : 2014
A Temperley-Lieb (TL) loop model is a Yang-Baxter integrable lattice model with nonlocal degrees of freedom. On a strip of width N ∈ ℕ, the evolution operator is the double-row transfer tangle D(u), an element of the TL algebra TL (β) with loop fugacity β = 2 cos λ, λ ∈ ℝ. Similarly, on a cylinder, the single-row transfer tangle T (u) is an element of the so-called enlarged periodic TL algebra. The logarithmic minimal models LM(p; p) comprise a subfamily of the TL loop models for which the crossing parameter λ = (p' - p)π=pis a rational multiple of π parameterized by coprime integers 1 ≤ p 2 takes the form of functional relations for D(u) and T (u) of polynomial degree p. These derive from ..View full abstract
Awarded by Australian Research Council
AMD is supported by the National Sciences and Engineering Research Council of Canada as a postdoctoral fellow. He is also grateful for support from the University of Queensland. JR is supported by the Australian Research Council under the Future Fellowship scheme, project number FT100100774. The authors thank Adam Ong, Yvan Saint-Aubin, Hubert Saleur, and Elena Tartaglia for comments and discussions. AMD and JR also thank Jean-Bernard Zuber and the LPTHE at Universite Pierre et Marie Curie, where part of this work was done, for their kind hospitality.