Retificação induzida por geometria em redes de spin

Abstract

The main point of this thesis is to explore how the geometry of a spin lattice can influence spin currents, and if a geometric asymmetry is able to induce rectification. Spin lattices in quantum closed systems, described by the XX model, with triangular geometry and without external magnetic field applied are investigated. The average occupation of spins on each site are analyzed through numerical simulations, considering different initial states, in order to verify propensities caused by the geometry. In all the addressed cases, the occupations were mostly on the side that presented more sites. Then, lattices with different geometries, including symmetric and asymmetric cases, in contact with reservoirs described by the XX and the XXZ models, with dynamics governed by the Lindblad master equation were explored. For those, homogeneous and non-homogeneous external magnetic field are applied and also different configurations for the reservoirs are considered. Through numerical simulation, currents and rectification coefficient are calculated for each case and the occurrence of rectification were observed in all cases with geometrical asymmetry when a non-homogeneous magnetic field was applied.