SF-Mott insulator transition and Wigner-mermin theorem

[wdlang]

i do not really understand wigmer-mermin theorem

in my impression, it states that there is no continuous symmetry breaking in 1d and 2d

so does wigner-mermin theorem rules out SF-Mott insulator transtion in 1d and 2d lattices ?

 

[Cthugha]

Do you mean Wagner-Mermin?

I do not know much about SF-Mott transitions, but as nobody answered yet, I will give it a try.

The theorem states in principle that two-dimensional systems with short-range interaction cannot break continuous symmetry spontaneously at finite temperature. This means there will be no spontaneous positional order of particles and no spontaneous magnetization in 2d.

However other kinds of transitions are not ruled out. For example Kosterlitz-Thouless transitions still work (vortices). Also 2d-systems, which are not in equilibrium can show phase transitions (polariton BECs, for example).

As I said before, I know next to nothing about Mott-transitions. However experimental realizations of the Mott transition in similar systems seem to exist:

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000100000012120402000001&idtype=cvips&gifs=yes

(Spielman et al., Phys. Rev. Lett. 100, 120402 (2008))

 

[wdlang]

Thanks a lot! Yes, there are a lot literatures on SF-Mott transition, the bose-hubbard model.

The most famous one being the PRB paper by Fisher.