# Spin-charge separation and Spin-Statistics relations

Usually, we associate the half-integer spin to fermion, and the integer spin to boson. And there are constraints like the Spin-Statistics relations.

However, in Spin–charge separation or the parton-construction techniques (Schwinger/Abrikosov boson/fermions, see also other webpages), we can separate a spin-1/2 charge-1 fermion to a spinon (with spin-1/2) and a holon (or called chargeon, with a charge-1).

It terms out that a spinon (with spin-1/2) in Spin–charge separation may be:

(1) bosonic spinon (with spin-1/2)!

(2) fermionic spinon (with spin-1/2).

In (1), even a spin-1/2 object called the spinon can be a boson!!!

I wonder what are the constraints on the Spin-charge separation, and how does this tie to the Spin-Statistics relations (in any dimensions, especially in 2+1d and 3+1d)?

• The spin-statistics relations are compatible with the spin-charge separation, since the later appears in low dimensions. See e.g. physics.stackexchange.com/questions/65767/… for more details. – FraSchelle Nov 15 '16 at 11:52
• @FraSchelle, But obviously I think wonderich meant that he/she considers the Schwnger/Abrikosov parton construction as spin charge separation, which works in 2+1 and 3+1 dim too. Perhaps it can be used in any dims. – user32229 Nov 15 '16 at 20:27
• The two questions are different. – user32229 Nov 15 '16 at 20:28
• @mysteriousness As far as I can see, the wikipedia page refers only to low dimensional systems. If Wonderich wants to make an other point, (s)he should make a clear question with explicit citation :-) Thank you anyways for the remark. – FraSchelle Nov 16 '16 at 9:33
• I think the Wikipage does not restrict to 1+1d. It only says 1+1d goes to Luttinger liquids (well-known.) Also he/she had referred to "parton-construction techniques (Schwinger/Abrikosov boson/fermions)." I am pretty sure that the community also uses that as Spin-charge separation. – user32229 Nov 16 '16 at 15:51