SSH model hamiltonian in momentum space

To change the basis i use the variables $zeta_k =frac{1}{sqrt{N}}sumlimits_{n=1}^{N}e^{inphi_k}a_n
~~~~~~~~~~
mu_k =frac{1}{sqrt{N}}sumlimits_{n=1}^{N}e^{inphi_k}b_n $

so i obtain$
H_{bulk}= sumlimits_{k}H(k)=sumlimits_{k}
begin{pmatrix}
zeta_k^dagger&mu_k^dagger
end{pmatrix}
begin{pmatrix}
0 & t_-+t_+e^{-ik}
t_-+t_+e^{ik} & 0
end{pmatrix}
begin{pmatrix}
zeta_k
mu_k
end{pmatrix}$ but this is the hamiltonian with this variables, what’s wrong?
and the hamiltonian now is a sum of hamiltonians with different momentum k, its suppose that i chose one and diagonalize it or what?
(sorry for my english)