Ordem Topológica e Transições de Fases Quânticas em Cadeias de Spins Interagentes

Abstract

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 comprehension 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 sophisticated isotropic and alternating Heisenberg Heisenberg. 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 chains1 2 − 1 2 −S −S#with S = 1 2,1, 3 2,2, 5 2 where we demonstrate that the zero-field critical points that arise in this class of models are universal and property 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, where we obtained a rich phase diagram of the model showing successive transitions of topological phases at zero fields. We investigate these transitions again implementing the finite size tangential scaling method, where we demonstrate that these transitions are also inherent and belong to the SU(2) Wess-Zumino-Witten class with ν = 2 3. Finally, we study global dissipation effects under the symmetry-protected topological ordering. To this end, we investigated the dissipative dynamics of the Affleck-Kennedy-Lieb-Tasaki model in one dimension from the Lindblad master equation. We show that for dissipation that preserves the time-reversal symmetry the topological ordering remains under dissipative dynamics even for high values of coupling between the physical system and the environment. However, for dissipations that break the time-reversal symmetry, we saw that the dissipative dynamics destroy the topological ordering.