The dilute Temperley–Lieb O(n = 1) loop model on a semi infinite strip: the ground state

Abstract

We consider the integrable dilute Temperley–Lieb (dTL) O(n = 1) loop model on a semi-infinite strip of finite width L. In the analogy with the Temperley–Lieb (TL) O(n = 1) loop model the ground state eigenvector of the transfer matrix is studied by means of a set of q-difference equations, sometimes called the qKZ equations. We compute some ground state components of the transfer matrix of the dTL model, and show that all ground state components can be recovered for arbitrary L using the qKZ equation and certain recurrence relation. The computations are done for generic open boundary conditions.