Groundstate finite-size corrections and dilogarithm identities for the twisted A1(1) , A2(1) and A2(2) models
(2021) Journal of Statistical Mechanics: Theory and Experiment — Vol. 2021, n° 3, p. 33105 (2021)
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- We consider the Y -systems satisfied by the A(1)1, A(1)2, 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 eiλ with the crossing parameter λ 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 Klümper and Pearce. The resulting expressions for c. 24Δ, where c is the central charge and Δ 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.
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Morin Duchesne, A., Klümper, A., & Pearce, P. A. (2021). Groundstate finite-size corrections and dilogarithm identities for the twisted A1(1) , A2(1) and A2(2) models. Journal of Statistical Mechanics: Theory and Experiment, 2021(3), 33105. https://doi.org/10.1088/1742-5468/abdc17 (Original work published 2021)