Construção de líquidos de spin quirais por junções de cadeias de spin

Abstract

In this thesis work, it was sought to present a new theoretical construction method of a chiral spin quantum liquid formed from Heisenberg spin chains. The spin chains, initially assembled in trios, were coupled in the form of Y junctions. In each Y junction, a chiral interaction was added between the three spins at the edges of each chain, in addition to the exchange interaction between neighbouring spins in the bulk of the chains. Through the previous study of an isolated Y junction its extension was investigated here by establishing the set of these junctions in the form of a hexagonal network of spin chains. The theoretical analysis was based on low energies using the bosonization technique and applying invariant boundary conditions to the bosonic modes or the chains’ spin currents. It was concluded, with the established chiral spin liquid, that the CSL is of the Kalmeyer-Laughlin type, which its elementary excitations correspond to spinons, fractional magnetic excitations of semonic statistics. The chiral spin liquid found is also accompanied by a quantized spin Hall conductance and edge modes at the network boundaries. The (gapped)spectrum of the spinons and the stability of the chiral liquid were studied through the backscattering perturbation between the chiral bosonic fields of neighboring hexagons and an effective tight-binding model for spinons. The theory was able to predict a phase transition when the spinon gap closes, resulting in the condensation of the spinons or the formation of a stable CSL. As a perspective, the method developed in this work can be extended to other topological phases of matter and eventually be useful in the application of topological quantum computing.