Algebraic geometry methods associated to the one-dimensional Hubbard model

Autor(es)

Martins, M. J.

• Tipo de documento: Artigo Científico
• Fonte: Nuclear Physics B; v. 907, p. 479-494, JUN 2016.
• Citações Web of Science: 1

Resumo

In this paper we study the covering vertex model of the one-dimensional Hubbard Hamiltonian constructed by Shastry in the realm of algebraic geometry. We show that the Lax operator sits in a genus one curve which is not isomorphic but only isogenous to the curve suitable for the AdS/CFT context. We provide an uniformization of the Lax operator in terms of ratios of theta functions allowing us to establish relativistic like properties such as crossing and unitarity. We show that the respective R-matrix weights lie on an Abelian surface being birational to the product of two elliptic curves with distinct J-invariants. One of the curves is isomorphic to that of the Lax operator but the other is solely fourfold isogenous. These results clarify the reason the R-matrix can not be written using only difference of spectral parameters of the Lax operator. (C) 2016 The Author. Published by Elsevier B.V. (AU)

• Processo FAPESP: 13/21466-8 - Sistemas integráveis e geometria algébrica
• Beneficiário: Marcio Jose Martins
• Modalidade de apoio: Auxílio à Pesquisa - Regular