| Grant number: | 19/11550-8 |
| Support type: | Scholarships in Brazil - Doctorate |
| Effective date (Start): | January 01, 2020 |
| Effective date (End): | March 31, 2022 |
| Field of knowledge: | Physical Sciences and Mathematics - Physics - Condensed Matter Physics |
| Principal Investigator: | Luis Gregório Godoy de Vasconcellos Dias da Silva |
| Grantee: | Raphael Levy Ruscio Castro Teixeira |
| Home Institution: | Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
Abstract The study of topological phases with exotic quasiparticles is one of the most active topics in condensed matter physics today. A well-studied recent example are Z_2-symmetric Majorana bound states in topological superconductors, with possible applications in topological quantum computation protocols. Another promising, albeit much less studied, example are Z_n-symmetric parafermionic modes, a natural generalization of Majorana quasiparticles, which could be used as the building blocks of an universal topological quantum computer''. This is not an easy task as out of the many proposals for the realization of parafermions in condensed matter systems , only a few works show the existence of topologically protected parafermionic states. This project intends to study the emergence of Z_n parfermionic states with n=3,4 in interacting 1D lattice models. As a first step, we will identify strongly interacting electronic (i.e., fermionic) models from exact mappings of parafermionic lattice models. We will then employ Density-Matrix Renormalization-Group (DMRG) calculations to investigate the topological phases of these models. To this end, we will calculate quantitities such as density correlations and other local and non-local properties which can be probed in experiments. We will also characterize the topological phases using the entanglement entropy of the system. As a result, we expect to identify both the type of interactions and the the range of parameters in which the topological phases appear in order to guide the experimental investigations in these systems. (AU) | |