%0 Journal Article
%T The dilute Temperley-Lieb O($n=1$) loop model on a semi infinite strip: the ground state
%A A. Garbali
%A B. Nienhuis
%J Physics
%D 2014
%I arXiv
%X 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 $q$KZ 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 $q$KZ equation and certain recurrence relation. The computations are done for generic open boundary conditions.
%U http://arxiv.org/abs/1411.7020v1