Continuum limit and symmetries of the periodic image spin chain Original Research Article

This paper is the first in a series devoted to the study of logarithmic conformal field theories (LCFT) in the bulk. Building on earlier work in the boundary case, our general strategy consists in analyzing the algebraic properties of lattice regularizations (quantum spin chains) of these theories. In the boundary case, a crucial step was the identification of the space of states as a bimodule over the Temperley–Lieb (TL) algebra and the quantum group image. The extension of this analysis in the bulk case involves considerable difficulties, since the image symmetry is partly lost, while the TL algebra is replaced by a much richer version (the Jones–Temperley–Lieb — JTL — algebra). Even the simplest case of the image spin chain — corresponding to the image symplectic fermions theory in the continuum limit — presents very rich aspects, which we will discuss in several papers.