A proof of selection rules for critical dense polymers
Alexi Morin-Duchesne · Journal of Physics A Mathematical and Theoretical · 2011
Among the lattice loop models defined by Pearce et al (2006 J. Stat. Mech. P11017), the model corresponding to critical dense polymers (β = 0) is the only one for which an inversion relation for the transfer matrix D N ( u ) was found by Pearce and Rasmussen (2007 J. Stat. Mech. P02015). From this result, they identified the set of possible eigenvalues for D N ( u ) and gave a conjecture for the degeneracies of its relevant eigenvalues in the link representation, in the sector with d defects. In this paper, we set out to prove this conjecture, using the homomorphism of the TL N (β) algebra between the loop model link representation and that of the XXZ model for β = −( q + q −1 ).