Hello everyone,
I am doing my project on topological phase transitions.
As a physics student, this topic can be useful for my research. Phase transitions due to symmetry breaking seem intuitive but not the topological ones for me. I would like to understand the realisations of this in the solid state like topological insulators or integer quantum hall effect.
This topic also fascinates me for its application in quantum computing. These states I guess has extra stability because ‘small perturbations’ won’t change the topological invariants, whatever they are!. This is important one main problem in this field to find a physical system where more qubits can be implemented without decohering.
I have not decided what research questions can be explored. If time permits I might be looking to what class of topological phases are possible or how can I use a particular topological state for implementing a quantum circuit.
Nick
February 19, 2018 — 22:53
I’m very unfamiliar with how topological phase transitions play a role in a condensed matter context. I’m really interested to know more about topological insulators. I had no idea topological phase transition were involved in integer quantum hall! Have you thought about also looking into fractional quantum hall or does it not apply there?
rsazdan
February 19, 2018 — 22:00
Speaking about qubits:) there is a lot about quantum knots https://inst.eecs.berkeley.edu/~cs191/fa09/presentations/topological.pdf but also this article by Abramsky https://arxiv.org/abs/0910.2737 and others…http://www.nature.com/scientificamerican/journal/v294/n4/box/scientificamerican0406-56_BX3.html
Brent
February 19, 2018 — 21:42
It seems to me like you could come at topological phase transitions from a number of angles. You could look at what physical characteristics you would expect from on i.e. how do you know one has occur, you could look at strategies for creating systems where this phase transitions occur, or focus on applications of of topological phase transitions. I hear about topological insulators all the time, but I don’t understand them. I hope you can you demystifying them for me if you go that route.
gljohns3
February 19, 2018 — 21:07
I’d like to know what you find out about topological invariants in qubits! I didn’t think a single electron spin state could be that interesting, but it is. You can actually represent a qubit via polarization states from E&M, which is kinda cool… I’m trying to get something more to say, but I’m not even sure how the phase of some material could be topological. I could see some being vector fields. Anyways, I’m looking forward to hearing about it.