Banca de DEFESA: LUAN FELIPE SANTOS MARTINS

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : LUAN FELIPE SANTOS MARTINS
DATE: 11/04/2023
TIME: 13:30
LOCAL: https://meet.google.com/azj-aztm-equ
TITLE:

Topological order and phase transitions in quantum interacting spin chains.

KEY WORDS:

Quantum spin chains, phase transitions, topological phases, scaling theory

PAGES: 137
BIG AREA: Ciências Exatas e da Terra
AREA: Física
SUBÁREA: Física da Matéria Condensada
SPECIALTY: Equação de Estado, Equilíbrio de Fases e Transições de Fase
SUMMARY:

In this work, we investigate topological orders and quantum phase transitions in distinct interacting spin models using numerical methods. We introduce the finite-size tangential scaling method, where we demonstrate its validation in the characterization of topological phase transitions between Haldane and Large-D phases in an anisotropic Heisenberg chain of spin S = 1. Our results were validated by theoretical theories of the critical exponent of the correlation length ν originated from a non-linear effective field theory σ. Next, we investigate the quantum phases and topological phase transitions for a class of tetramer ferrimagnetic models (S1 − S1 − S2 − S2) with isotropic and alternating Heisenberg interactions. We first investigate the case S1 = 1 2 and S2 = 5 2 where we obtain the phase diagram of the model and investigate the quantum phases from different magnetization curves. We characterize a critical point of the phase diagram using the finite-size tangential scaling method, where we have a topological phase transition of critical exponent ν = 2 3 . Next, we investigate the universality of topological phase transitions for a class of ferrimagnetic chains where we demonstrate that the zero-field critical points that arise in this class of models are universal and belong to the universality class SU(2) Wess-Zumino-Witten with ν = 2 3 . Finally, we investigated another tetramer ferrimagnetic chain with S1 = 1 and S2 = 3 2 , obtaining a rich phase diagram of the model showing successive transitions of topological phases at zero field. We investigate these transitions again implementing the finite size tangential scaling method, where we demonstrate that these transitions are also universal and belong to the SU(2) Wess-Zumino-Witten class with ν = 2 3 . Finally, we investigate the role of distinct dissipations in the symmetry-protected topological order given by the Affleck-Kennedy-Lieb-Tasaki model in one dimension using tensor network methods. We show that for asymmetric dissipations with respect to time-reversal symmetry the nontrivial topological ordering is destroyed with increasing dissipation intensity γ. For the case of symmetric dissipation, we saw that the model’s symmetry-protected topological phase is maintained, validated by measurements of the order parameter string, purity Γn, and analyzing the Schmidt spectrum. It is worth mentioning that we identified the degeneracy pattern in the Schmidt spectrum of the model’s density matrix in the steady state, as it is possible to observe in the entanglement spectrum in the case of non-trivial topological phases for pure states. Our results validate the argument that we obtained a dissipative symmetry-protected topological phase and that can be characterized by tools also used for the case of pure states.

BANKING MEMBERS:
Presidente - 1120933 - MARCELO LEITE LYRA
Interno(a) - 2621034 - MARIA SOCORRO SEIXAS PEREIRA
Externo(a) à Instituição - RODRIGO G. PEREIRA - UFRN
Externo(a) à Instituição - RENE RODRIGUES MONTENEGRO FILHO - UFPE
Externo(a) à Instituição - Adauto José Ferreira de Souza - UFRPE