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For spin 1/2 particles, I know how to write the representations of the symmetry operators
for instance T=i\sigma^{y}K (time reversal operator)
C_{3}=exp(i(\pi/3)\sigma^{z}) (three fold rotation symmetry) etc.
My question is how do we generalize this to, let's say, a basis of four component spinor with spins localized on two sites a and b
(|a, up>, |a, down>, |b, up>, |b, down>)^{T}
Is it a direct product i\sigma^{y}K \otimes i\sigma^{y}K
Or i\sigma^{y}K \otimes I_{2 \times 2}
Or is it something else?
It would be wonderful if you could point to any references.
for instance T=i\sigma^{y}K (time reversal operator)
C_{3}=exp(i(\pi/3)\sigma^{z}) (three fold rotation symmetry) etc.
My question is how do we generalize this to, let's say, a basis of four component spinor with spins localized on two sites a and b
(|a, up>, |a, down>, |b, up>, |b, down>)^{T}
Is it a direct product i\sigma^{y}K \otimes i\sigma^{y}K
Or i\sigma^{y}K \otimes I_{2 \times 2}
Or is it something else?
It would be wonderful if you could point to any references.