Integrable sistems and algebraic geometry

• Grant number: 13/21466-8
• Support Opportunities: Regular Research Grants
• Start date: March 01, 2014
• End date: February 29, 2016
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Marcio Jose Martins
• Grantee: Marcio Jose Martins
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The main purpose of this research is to establish a new approach to uncover relevant exactly two-dimensional solved models by exploring a direct relationship with the theory of Algebraic Geometry. We intend to develop a systematic manner to solve a high number of polynomial equations derived from the Yang-Baxter equation by combining analytical techniques with computational algorithms used in problems of Commutative Algebra. We hope that this approach will lead us to discover new families of integrable models lying in hypersurfaces whose potential divisors are non-rational varieties which so far are very rare in the literature. Within this new perspective we intend to investigate vertex models of Statistical Mechanics as well as certain generalizations of the Hubbard model being of interest of Condensed Matter Physics. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MARTINS, M. J.. An integrable nineteen vertex model lying on a hypersurface. Nuclear Physics B, v. 892, p. 306-336, MAR 2015. (13/21466-8)

MARTINS, M. J.. Algebraic geometry methods associated to the one-dimensional Hubbard model. Nuclear Physics B, v. 907, p. 479-494, JUN 2016. (13/21466-8)