Creating non-local operators as sum of local operators

[Kaanonder]

I’m trying to define a set of non-local operators such as

\tilde{c}_{i}=\sum_j f(i-j) c_{ j}

with some function f and the sum over the full lattice. My goal is to first define such a \tilde{c}_{i} which I can then use to construct interactions in a Hamiltonian.

I could try to do this in the Hamiltonian directly but it get’s very cumbersome so I’d like to first define \tilde{c}_{i}, then plug it into my Hamiltonian. How should I go about this?

Thanks very much!