Quantum loop subalgebra and eigenvectors of the superintegrable chiral Potts transfer matrices

Au Yang Helen*, Jacques H.H. Perk

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    It has been shown in earlier works that for Q = 0 and L a multiple of N, the ground state sector eigenspace of the superintegrable τ 2(tq) model is highly degenerate and is generated by a quantum loop algebra L(sl2). Furthermore, this loop algebra can be decomposed into r = (N-1)L/N simple sl2algebras. For Q ≠ 0, we shall show here that the corresponding eigenspace of τ2(t q) is still highly degenerate, but splits into two spaces, each containing 2r-1independent eigenvectors. The generators for the sl2subalgebras, and also for the quantum loop subalgebra, are given generalizing those in the Q = 0 case. However, the Serre relations for the generators of the loop subalgebra are only proven for some states, tested on small systems and conjectured otherwise. Assuming their validity we construct the eigenvectors of the Q ≠ 0 ground state sectors for the transfer matrix of the superintegrable chiral Potts model.

    Original languageEnglish
    Article number025205
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume44
    Issue number2
    DOIs
    Publication statusPublished - 14 Jan 2011

    Fingerprint

    Dive into the research topics of 'Quantum loop subalgebra and eigenvectors of the superintegrable chiral Potts transfer matrices'. Together they form a unique fingerprint.

    Cite this