Processos de magnetização e emaranha-mento quântico no tubo triangular de Spins -½ frustrados.

Abstract

This thesis is dedicated to the analytical and numerical study of quantum entanglement and nonlocality in strongly correlated quantum spin tube models in connection with various thermodynamic properties and magnetization processes. More specifically, the study builds on the analysis of the behavior of these physical quantities within a particular spinning network that includes competitive interactions and quantum fluctuations known as a three-leg spins ladder or triangular spin tube, due to the periodic boundary conditions imposed on the three spins that form the Heisenberg steps of this network. In systems with this structure described above, magnetization plateaus are formed due to the competition imposed by the geometric frustration that the network imposes on the spins and the applied external field. Such competition is the mechanism that defines the orientation of the magnetic domains that the network will present, which within specific regions of the network parameters space create regions where there is a discontinuous response of local magnetization to external field variations, such regions are known as magnetization plateaus. To evaluate the frustrated spin- ½ Ising-Heisenberg triangular tube consisting of a spin tube formed by triangular unit cells with 3 spins-½ interconnected by Heisenberg couplings between neighboring first spins and the pairs of neighboring first spins belonging to the different cells have their interaction intermediated through classical Ising couplings, an exact analytical procedure, known as a transfer-matrix technique, was used to obtain the analytical solutions for various thermodynamic properties of the model, including magnetization, specific heat and magnetization profiles. These quantities were evaluated as a function of temperature, external magnetic field and the relevant couplings. However, it was necessary to apply a different methodology to obtain thermodynamic measurements for the other model proposed in this thesis: the frustrated spin- ½ Heisenberg triangular tube, which consists of a spin tube with similar structure to the previous one, except that the pairs of the first neighboring spins belonging to the different cells interact through Heisenberg-type quantum connections. In this case, a numerical procedure known as the quantum density matrix renormalization group method, known as DMRG, is used to obtain the ground state diagrams, magnetization processes, and bipartite quantum entanglement of the Heisenberg triangular tubes as a function of the external magnetic field and the relevant couplings. In both models, the magnetization curves exhibit discontinuous magnetization jumps and intermediate plateaus due to discontinuous phase transitions induced by the external field, These transitions are also reflected in the exotic behavior of some thermodynamic quantities of the models, such as the presence of a striking low temperature peak for the specific heat curve and a highlighted magnetocaloric effect.