Topological Phase: Definition & Examples

[complement]

Hi there!

Can anybody tell me, if generically any system, which is solely described by a topological field theory, resides in a topological phase? I can't find any clear notion of topological phase. Only topological phase of matter, but I mean any kind of system.

Thanks for your help.

 

[atyy]

Levin gives a definition in this talk. He defines a topological phase as being gapped, having a ground state degeneracy that depends only on the topology of the manifold that the system is placed on, and has fractional statistics.

Similar definitions are given by Nayak et al (section III.A) and Hansson et al (section B of the introduction).

Moore's notes contain a different definition of topological phase ('Thouless phases'), which he distinguishes from the definition of topological phase ('Wen-type phases') used by Levin, Nayak and Hansson.

 

[member 11137]

Levin gives a definition in this talk. He defines a topological phase as being gapped, having a ground state degeneracy that depends only on the topology of the manifold that the system is placed on, and has fractional statistics.

Similar definitions are given by Nayak et al (section III.A) and Hansson et al (section B of the introduction).

Moore's notes contain a different definition of topological phase ('Thouless phases'), which he distinguishes from the definition of topological phase ('Wen-type phases') used by Levin, Nayak and Hansson.

Very interesting. Do you know some references explaining the derivation of the CS Lagrangian (e.g. wenphases.pdf, page 1, (5))?

 

[Physics Monkey]

At what level would you like the explanation?

 

[complement]

full scale please :)

 

[member 11137]

At what level would you like the explanation?

Well, what can I say? The level of an amateur with a relatively good mathematical background. I was wondering about the formalism of that Lagrangian and interested by the fact that it is interpreted as a "topological one". I know that CS theories are developped in spaces with an odd number of dimensions (N = 3, 5...). Is there also in the published literature a derivation of a similar expression for spaces with an even number of dimensions (e.g. N = 4)?