- #1
Petar Mali
- 290
- 0
Tha classical ground state is Ne\'{e}l state: every spin up is surrounded by nearest neighbours which are down, and vice versa. To give them a name, denote the spins down the [tex]A[/tex] sublattice, and the spins up the [tex]B[/tex] sublattice. Perform a canonical transformation on the [tex]B[/tex] (but not on the [tex]A[/tex] spins: rotate them by [tex]180^{\circ}[/tex] about the [tex]\hat{S}^x[/tex] axis,
[tex]\hat{S}_j^{\pm}\rightarrow +\hat{S}_j^{\mp}[/tex]
[tex]\hat{S}_j^z \rightarrow -\hat{S}_j^z[/tex] [tex](j in B)[/tex]
Can you explain me this transformation with more details? I can't see why relations
[tex]\hat{S}_j^{\pm}\rightarrow +\hat{S}_j^{\mp}[/tex]
[tex]\hat{S}_j^z \rightarrow -\hat{S}_j^z[/tex] [tex](j in B)[/tex]
are satisfied?
[tex]\hat{S}_j^{\pm}\rightarrow +\hat{S}_j^{\mp}[/tex]
[tex]\hat{S}_j^z \rightarrow -\hat{S}_j^z[/tex] [tex](j in B)[/tex]
Can you explain me this transformation with more details? I can't see why relations
[tex]\hat{S}_j^{\pm}\rightarrow +\hat{S}_j^{\mp}[/tex]
[tex]\hat{S}_j^z \rightarrow -\hat{S}_j^z[/tex] [tex](j in B)[/tex]
are satisfied?