Publication:
Topological Phases of Matter and Open Quantum Systems

Loading...
Thumbnail Image
Official URL
Full text at PDC
Publication Date
2017-07-31
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad Complutense de Madrid
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
The growing field of topological orders has been extensively studied both form the communities of condensed matter and quantum simulation. However, very little is known about the fate of topological order in the presence of disturbing effects such as external noise or dissipation. In the first part of this thesis, we start by studying how the edge states of a topological insulator become unstable when interacting with thermal baths. Motivated by these results, we generalise the notion of Chern insulators from the well-known Hamiltonian case to Liouvillian dynamics. We achieve this goal by defining a new topological witness that is still related to the quantum Hall conductivity at finite temperature. The mixed character of edge states is also well captured by our formalism, and explicit models for topological insulators and dissipative channels are considered. Additionally, we find new topological phases that remain quantised at finite temperature. The construction is based on the Uhlmann phase, a geometric quantum phase defined for general density matrices. Using this new tool, we are able to characterise topological insulators and superconductors at finite temperature both in one and two spatial dimensions. From the experimental side, we propose a state-independent protocol to measure the topological Uhlmann phase in the context of quantum simulation. Symmetry-protected topological orders have traditionally emerged from shortrange interactions. It remains very much unknown what the role played by longrange interactions is, within the physics of these topological systems. In the second part of this thesis, we analyse how topological superconducting phases are affected by the inclusion of long-range couplings. Remarkably, we unveil new topological quasi-particles due to long-range interactions, that were absent in short-range models. We also study how topological invariants are modified by the presence of long-range effects. In the appendix section of the thesis, we explore new numerical methods for driven-dissipative phase transitions. We consider quantum systems with a dissipative term driving the system into a non-equilibrium steady state. The inclusion of short-range fluctuations out-of-equilibrium deeply modifies the shape of the phase-diagram, something never observed in equilibrium thermodynamics.
Una transición de fase es una transformación entre dos estados de la materia con propiedades físicas diferentes, por ejemplo cuando el agua líquida se convierte en hielo. Tradicionalmente, la física de las transiciones de fase ha sido perfectamente descrita por la teoría de Landau. Esta teoría propone la existencia de un parámetro de orden local que es capaz de distinguir entre dos fases distintas. Además, al atravesar la transición de fase se rompe espontáneamente una simetría del sistema. A partir de los años 80 se empezaron a encontrar un tipo de transiciones de fase que no estaban bien descritas por la teoría de Landau. Estas fases de la materia se denominan órdenes topológicos y constituyen el principal objeto de esta tesis doctoral. Para estas transiciones no existe un parámetro de orden local que pueda distinguir entre fases con propiedades físicas distintas. Por el contrario, vienen caracterizadas por un parámetro de orden global que es capaz de retener la información topológica del sistema. La otra principal diferencia con respecto a las transiciones de orden, descritas por la teoría de Landau, es el papel que juegan las simetrías. En las transiciones de fase topológicas, cuando se cambia de una fase a otra, no se rompe ninguna simetría. De manera adicional, las fases topológicas de la materia vienen caracterizadas por un conjunto de propiedades distintivas: (1) el estado fundamental está separado por un gap del resto de excitaciones y está degenerado, (2) el sistema presenta estados gapless localizados en el borde, (3) las excitaciones son anyones con estadística exótica, etc...
Description
Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Física Teórica I Física Teórica II (Métodos Matemáticos de la física), leída el 02/11/2016. Tesis formato europeo (compendio de artículos)
Unesco subjects
Keywords
Citation
Collections