Critical Phenomena in Quasicrystals

• Grant number: 25/27881-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2026
• End date: December 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: Eric de Castro e Andrade
• Grantee: Pedro Loureiro Barboza
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 21/06629-4 - Electronic correlations in quantum materials: inhomogeneities and frustration, AP.JP2

Abstract

Since their discovery, quasicrystals have driven the extension of established physical theories to include systems with long-range non-periodic ordering. While the initial focus was on their structure and basic electronic properties, the recent realization of correlated phases in platforms such as Moiré superlattices and optical lattices has motivated the community to investigate the emergent properties resulting from this non-periodic arrangement. This project proposes studying the Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional quasicrystalline tilings. The central focus will be to investigate how the transition is modified by the introduction of terms that break the spin rotation symmetry. These terms will be chosen to be compatible with the non-crystallographic rotational symmetries inherent to these systems, with the aim of understanding the direct influence of the quasi-periodic geometry on critical phenomena. (AU)