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 $q$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.

25 pages, 30 figures, Updated version

References in corpus (2)

• Exact spin quantum Hall current between boundaries of a lattice strip
• The dilute Temperley-Lieb O($n=1$) loop model on a semi infinite strip: the sum rule

Cited by in corpus (3)

• Critical points of Potts and O($N$) models from eigenvalue identities in periodic Temperley-Lieb algebras
• The dilute Temperley-Lieb O($n=1$) loop model on a semi infinite strip: the sum rule
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