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

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

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

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  What's the meaning of "topological" in "symmetry protected topological phase"

+ 8 like - 0 dislike
3353 views

I am trying to understand the symmetry protected topological phase. Most papers only explain the symmetry but none of them explain the meaning of "topological". My question is : What's the meaning of "topological" in "symmetry protected topological phase"?


This post imported from StackExchange Physics at 2014-04-05 04:39 (UCT), posted by SE-user fangniuwawa

asked Sep 18, 2013 in Theoretical Physics by fangniuwawa (65 points) [ revision history ]
retagged Apr 5, 2014 by Xiao-Gang Wen
Perhaps this can (partially) answer your question: physics.stackexchange.com/questions/57179/…. I can provide additional details if necessary.

This post imported from StackExchange Physics at 2014-04-05 04:39 (UCT), posted by SE-user NanoPhys

1 Answer

+ 4 like - 0 dislike

The follow article directly address your question (which is a very good question):

http://physicsoverflow.org/13018/reconciling-topological-insulators-and-topological-order

The article explains the different meaning of "topological" in "topological insulators" and "topological order".

You observed that most papers only explain the symmetry but none of them explain the meaning of "topological". That is a very good observation. Most papers do not talk about "topological" because the interacting "symmetry protected topological phase" is not topological (ie have trivial topological order and short-range entanglement). We call such short-range entangled phases "topological" because some well known examples of them, such as the Haldane phase and topoloical insulator, were refered as "topological" phases. 


This post imported from StackExchange Physics at 2014-04-05 04:39 (UCT), posted by SE-user Xiao-Gang Wen

answered Oct 6, 2013 by Xiao-Gang Wen (3,485 points) [ revision history ]
edited Apr 5, 2014 by Xiao-Gang Wen

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).
Please complete the anti-spam verification




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

Your rights
...