• 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.


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


(propose a free ad)

Site Statistics

143 submissions , 120 unreviewed
3,899 questions , 1,377 unanswered
4,837 answers , 20,500 comments
1,470 users with positive rep
495 active unimported users
More ...

  Questions on the elementary excitations in the resonating-valence-bond(RVB) states?

+ 5 like - 0 dislike

It is known that the RVB states can support spin-charge separations and its elementary excitations are spinons and holons. But it seems that there are some different possibilities for the nature of the statistics of the spinons and holons. Specifically, (1) spinons are fermions while holons are bosons(Kivelson et al);(2)spinons are bosons while holons are fermions(Read et al);(3)spinons and holons are both semions obeying fractional statistics(Laughlin et al).

Do we now have a commonly accepted view for one of the above three possibilities? Or do the quasiparticle statistics depend on the details(e.g. which kind) of the RVB wave functions?

Furthermore, assume RVB states as the ground-states of the antiferromagnetic Heisenberg model, and when we use $t-J$ model to study the lightly doped Mott insulator, for the possibility (1), it's reasonable to adopt slave-boson formalism, while for the possibility (2), it's reasonable to adopt slave-fermion formalism, right? But for the possibility (3), what kind of slave-particle formalism we should adopt? This part may be related to my previous question.

Thanks in advance.

This post imported from StackExchange Physics at 2014-03-09 08:39 (UCT), posted by SE-user K-boy

asked Dec 8, 2013 in Theoretical Physics by Kai Li (975 points) [ revision history ]
edited Apr 6, 2015 by Kai Li
@ Xiao-Gang Wen Thank you very much.

This post imported from StackExchange Physics at 2014-03-09 08:39 (UCT), posted by SE-user K-boy

1 Answer

+ 4 like - 0 dislike

From the answer


we see the RVB state does not refer to one state, it can refer to many different states (with different topological orders). The RVB states with different topological orders can have different properties. There is a RVB state (with a $Z_2$ topological order) where the spinons are fermions while the holons are bosons. There is another RVB state (with a different $Z_2$ topological order)  where spinons are bosons while holons are fermions. There is a third RVB state (chiral spin liquid) where spinons and holons are both semions obeying fractional statistics.

answered Apr 4, 2014 by Xiao-Gang Wen (3,319 points) [ no revision ]

@Xiao-Gang Wen Thank you Prof.Wen. What about a chiral spin liquid with a $Z_2$ topological order ?

Chiral spin liquid can also be described by the slave-fermion formalism, if you put the fermions into a mean-field ansatz with nontrivial topological band structure (i.e. Chern number).

@Meng Yes, I agree with you. Do you know some existing studies on the $Z_2$ chiral spin liquid (a $Z_2$ spin-liquid with broken time-reversal symmetry) ? Thanks a lot!

There is a large body of literature on chiral spin liquid. A recent VMC study is http://journals.aps.org/prb/abstract/10.1103/PhysRevB.91.041124, and you can find in the references of the paper many recent (exact) numerical studies of chiral spin liquid in Heisenberg models on the kagome lattice.

As to my first comment, I think I can answer it now: The TR symmetry is NOT essential to the topological order for a $Z_2$ SL, since the topological degeneracy of a $Z_2$ SL on a torus is always 4 while the total ground-state degeneracy (TGSD) is TGSD$=2\times 4$ for the spontaneous TR breaking $Z_2$ SL ($Z_2$ CSL) and TGSD$=4$ for the TR symmetric $Z_2$ SL.

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:
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