The 8-vertex model, the toric code and quantum information

• Grant number: 23/18381-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2024
• End date: February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Rodrigo Bissacot Proença
• Grantee: Arthur Ferreira Domont Sobreira
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 16/25053-8 - Dynamics and geometry in low dimensions, AP.TEM

Abstract

The research project will focus on studying the 8-vertex model and how it is connected to other lattice systems. I am especially interested in understanding its relation to Kitaev's toric code model, one of the greatest examples of topological quantum codes. The project therefore intends to research in detail the 8-vertex model, the toric code, and its correlation inequalities, which were explored in great depth by Björnberg and Lees in [2]. Therefore, in addition to advancing my knowledge in the field and developing the techniques needed, another goal set is to read this paper carefully and in completeness.