Exact correlations in topological quantum chains

Free fermion chains are particularly simple exactly solvable models. Despite this, typically one can find closed expressions for physically important correlators only in certain asymptotic limits. For a particular class of chains, I will show that we can apply Day's formula and Gorodetsky's formula for Toeplitz determinants with rational generating function. This leads to simple closed expressions for determinantal order parameters and the characteristic polynomial of the correlation matrix. The latter result allows us to prove that the ground state of the chain has an exact matrix-product state representation.