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
5,054 questions , 2,207 unanswered
5,345 answers , 22,720 comments
1,470 users with positive rep
818 active unimported users
More ...

  What are examples of condensed matter systems of all 10 classes listed in the 10-fold way?

+ 2 like - 0 dislike
588 views

The tenfold way is a mathematical classification of Hamiltonians used in condensed matter physics, based on their symmetries.  While it has connections to many mathematical subjects, I'd like to know examples of real-world condensed matter systems of all ten kinds.  Nine kinds are characterized by choosing one of these 3 options:

* antiunitary time-reversal symmetry with $T^2 = 1$, with $T^2 = -1$, or no such symmetry.

and one of these 3 options:

* antiunitary charge conjugation symmetry with $C^2 = 1$, with $C^2 = -1$, or no such symmetry.

Charge conjugation symmetry in condensed matter physics is usually a symmetry between particles (e.g. electrons or quasiparticles of some sort) and holes.   The tenth kind has unitary "$S$" symmetry, a symmetry that simultaneously reverses the direction of time and interchanges particles and holes.  Since it is unitary we can assume without loss of generality that $S^2 = 1$.

**What are examples of real-world condensed matter systems of all ten kinds?**

asked Jan 23, 2023 in Q&A by John Baez (405 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:
p$\hbar\varnothing$sicsOverflow
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
...