A proof of selection rules for critical dense polymers

作者：Morin Duchesne Alexi^*

来源：Journal of Physics A-Mathematical and Theoretical, 2011, 44(49): 495003.

DOI：10.1088/1751-8113/44/49/495003

Among the lattice loop models defined by Pearce et al (2006 J. Stat. Mech. P11017), the model corresponding to critical dense polymers (beta = 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)(beta) algebra between the loop model link representation and that of the XXZ model for beta = -(q + q(-1)).

• 出版日期2011-12-9