Técnicas de diagonilização exata de modelos quânticos unidimensionais: a transformação de Jordan-Wigner e o Ansatz de Bethe

Abstract

In the present work the XY and Heisenberg models in one dimension are studied. They are useful to describe certain physical phenomena, such as the magnetic properties of materials. The Hamiltonian of the XY model is completely diagonalized and it was possible to get some thermodynamic properties of a system described by the model, such as free energy and magnetization. We observe here in this system the presence of a phase transition when changing the magnetic field inthe z-direction. For the Heisenberg model, it is described in this work a procedure that allows one to completely diagonalize the Hamiltonian. There is an interesting similarity between most of the eigenvalues of the Heisenberg Hamiltonian and the eigenvalues of the XY Hamiltonian in the thermodynamic limit.