Quantum phase transitions in one-dimensional integrable systems

• Grant number: 24/07671-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2024
• End date: December 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: José Abel Hoyos Neto
• Grantee: Angelo Antonio Vernaschi Zampronio
• Host Institution: Instituto de Física de São Carlos (IFSC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Matter organizes itself in complex ways at low energies. Commonly, the physical state of matter at the lowest energy/temperature is less symmetrical and more complex, with new emergent properties that characterize it. These emergent properties are inherent to phase transitions. Impressively, matter can also transition from one state to another even at zero temperature. In this case, it is said that a quantum phase transition has occurred. Here, the competition is between the interactions of matter and quantum fluctuations. The latter can be so strong that they destroy organized structures. Nowadays, a significant fraction of the field of condensed matter physics is dedicated to studying this phenomenon both theoretically and experimentally. The present project is set within this context. The student will need to become familiar with the study of quantum phase transitions. To this end, we propose the study of a paradigmatic model: the transverse field Ising chain, taking the limit of ferromagnetic interactions between neighboring spins as much greater or much less than the quantum fluctuations, exploring the emergent properties and phase transition within this range.This study will be conducted using the free fermion technique. The Hamiltonian of the aforementioned model, through the Wigner-Jordan transformation, can be mapped into a system of non-interacting fermions, and many results can be obtained analytically. To achieve this, the student will also need to study second quantization to become familiar with the concepts associated with free fermion systems.