Given a tight binding model with Hamiltonian
$H= \sum_{i(even)}t[c_{i+1}^\dagger c_i+h.c]$
containing even indices only, how can we find out the dispersion relation?
Attempt:
My guess is that the dispersion relation is just $\frac{-2tcos(ka)}{2}$ i.e. half the regular tight binding model. I could not find the source for dispersion relation with two different hopping amplitudes. If I had, I would just replace one with zero.
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