Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

Please welcome our new moderators!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

122 submissions , 103 unreviewed
3,497 questions , 1,172 unanswered
4,543 answers , 19,337 comments
1,470 users with positive rep
407 active unimported users
More ...

Can anyons emerge from momentum-space other than spatial dimensions?

+ 5 like - 0 dislike
38 views

So far in condensed matter physics, I only know anyons(abelian or nonabelian) can emerge as quasiparticles in 2D real-space.

But is there any possibility to construct anyons in momentum-space ? And what about the braiding, fusion rules in momentum-space ? I mean do anyons always live in real-space rather than in momentum-space ?

Maybe this is a trivial question, thank you very much.

This post imported from StackExchange Physics at 2014-03-09 08:45 (UCT), posted by SE-user K-boy
asked Jul 14, 2013 in Theoretical Physics by Kai Li (975 points) [ no revision ]

1 Answer

+ 2 like - 0 dislike

I was wondering something similar few month ago. Then I concluded that most of the topological staffs appear at the boundary between two different topological sector. A sector being characterised by a Chern number, or if you prefer a topological charge, one needs a boundary / an interface between two systems characterised by different topological charge.

A $k$-space (or momentum, or reciprocal, or Fourier, ...) is well defined only for periodic boundary conditions. The fact that the $x \leftrightarrow k$ is a Fourier transform imposes a periodicity in $x$ or in $k$. That's the stringent condition under which $k$ is a good quantum number. Note that we can still define some quasi-$k$ for disordered media. So we could not in principle define a $k$-space when a system has boundary. Note that infinite system are usually closed by periodic boundary condition, also called Born-von-Karman conditions.

I'm not aware so much about anyons (I'm still learning about that) but I believe they (almost all of them ? all of them ? I don't know) appear due to boundary conditions in condensed matter, for the reason I gave about the topological charge transition. So I believe it should be impossible to define anyons in $k$-space, for the simple reason that the $k$-space is not a correct description of the matter when anyons exist.

I would really appreciate comments/critics about what I said, especially if it's (partially) wrong.

This post imported from StackExchange Physics at 2014-03-09 08:45 (UCT), posted by SE-user Oaoa
answered Jul 14, 2013 by Oaoa (50 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
$\varnothing\hbar$ysicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...