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## Main Question or Discussion Point

I've found the simplest hopping Hamiltonian for fermions (diagonal in momentum space) has a so-called Fermi sea ground state.

[tex] H = -2 t \sum_k \cos(k) f^+_k f_k [/tex]

(t is some parameter in units of energy).

How do I evaluate the expected value of the spin exchange operator [tex] S_x \cdot S_{x+1} [/tex] in this state? I am having trouble because the ground state obvious in the momentum basis, and it is not written in the position basis.

[tex] H = -2 t \sum_k \cos(k) f^+_k f_k [/tex]

(t is some parameter in units of energy).

How do I evaluate the expected value of the spin exchange operator [tex] S_x \cdot S_{x+1} [/tex] in this state? I am having trouble because the ground state obvious in the momentum basis, and it is not written in the position basis.