Groundstate finite-size corrections and dilogarithm identities for the twisted A1(1), A2(1) and A2(2) models

We consider the Y-systems satisfied by the A(1)((1)), A(2)((1)) and A(2)((2)) vertex and loop models at roots of unity with twisted boundary conditions on the cylinder. The vertex models are the 6-, 15- and Izergin-Korepin 19-vertex models respectively. The corresponding loop models are the dense, fully packed and dilute Temperley-Lieb loop models respectively. For all three models, our focus is on roots of unity values of e(i lambda) with the crossing parameter lambda corresponding to the principal and dual series of these models. Converting the known functional equations to nonlinear integral equations in the form of thermodynamic Bethe ansatz equations, we solve the Y-systems for the finite-size 1/N corrections to the groundstate eigenvalue following the methods of Klumper and Pearce. The resulting expressions for c - 24 Delta where c is the central charge and Delta is the conformal weight associated with the groundstate, are simplified using various dilogarithm identities. Our analytic results are in agreement with previous results obtained by different methods.

Automated summary

The study focuses on the Y-systems satisfied by the A(1)((1)), A(2)((1)), and A(2)((2)) vertex and loop models at roots of unity, corresponding to the dense, fully packed, and dilute Temperley-Lieb loop models. By converting known functional equations to nonlinear integral equations and simplifying the resulting expressions using various dilogarithm identities, the finite-size 1/N corrections to the groundstate eigenvalue are solved, showing agreement with previous results obtained by different methods.