Quantum Hall States on Deformed Tori

Carolina Branco Albergaria Paiva

Key information

Authors:

Carolina Branco Albergaria Paiva (Carolina Branco Albergaria Paiva)

Supervisors:

Bruno Miguel Santos Mera (Bruno Miguel Santos Mera); João Luís Pimentel Nunes (João Luís Pimentel Nunes)

Published in

September 9, 2022

Abstract

In the present thesis we continue the work of Gabriel Matos and Paulo Mourão, in which imaginary time Hamiltonian flows were used to deform the geometry of the quantum Hall effect on the plane, cylinder and sphere. In their work formulas for the evolution of Laughlin states were obtained by lifting the deformations to the Hilbert space (using tecnhiques of geometric quantization) via a generalized coherent state transform. Our goal is to do the same for the torus. We are then able to obtain expressions for the evolution of the Laughlin states, making it possible to compare these with the results found in the literature, and computationally we can obtain the particles' density profiles. We also explore the viscosity of these systems including spin, obtaining an expression for the dependency of the viscosity in terms of the spin of the particles and the modular parameter of the torus. This result, not present in the literature yet, is consistent with the spinless result found in the literature. Finally, the evolution and the particles density profile in the case where the geometry of the torus is not flat is analyzed.