Mesure géométrique de l'intrication de la chaîne d'Ising quantique

Details

Supervisors

Walmsley Hagendorf, Christian

Faculty

Faculté des sciences

Degree label

Master [120] en sciences physiques, à finalité approfondie

Abstract

enIn recent decades, quantum entanglement has proven to be an essential tool in the study of phase transitions and the development of quantum technologies. This thesis is dedicated to the analysis of entanglement within the quantum Ising chain. First, an exact diagonalisation of its Hamiltonian is performed for two types of boundary conditions: open and periodic. Subsequently, the geometric measure of entanglement of its ground state is calculated. The influence of the choice of boundary conditions on this measure is analysed for finite-size chains. The behaviour of the entanglement density, as well as that of its derivative with respect to the applied field, is also investigated in the thermodynamic limit. This analysis is then extended to the XX and XY chains for comparative purposes. The results suggest that the geometric measure of entanglement constitutes a relevant indicator of the presence of quantum phase transitions in multipartite systems. Finally, the study is completed by a comparison of the entanglement densities of the first excited state of the Ising chain for both types of boundary conditions.