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2

The model of Levin and Gu is built out of products of the spin-1/2 operators $S_i^x$, $S_i^y$ and $S_i^z$ at each site $i$. These operators commute with each other at different sites ($[S_i^\alpha, S_j^\beta] = 0$ for $i \neq j$), which is the reason why we say this model is bosonic, and the SPT phases in this model are bosonic SPT's. By constrast, a ...

4

Well, $1/2\otimes1/2=0\oplus1$, so a system with two fermions has integer spin. But it is still a two fermion system, and therefore its wavefunction must be antisymmetric, as usual. This is not specific to Cooper pairs, but is basic Quantum Mechanics... [what is specific to Cooper pairs is that their size is $\gg a_0$, which means they are highly ...

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First, observe that the Slater determinant you have written down is the linear combination of the singlet state and the z-spin-0 state of the triplet. Vice versa, you can produce the singlet and triplet states as linear combinations of Slater determinants. Whether you prefer the Slater determinant or the singlet/triplet formalism for writing down your ...

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