Ivan Damnjanović

A polynomial GCD certificate for exact flat bands in finite-range Bloch Hamiltonians

Abstract We formulate a polynomial GCD certificate for exact flat bands in finite-range periodic tight-binding Hamiltonians. Writing the characteristic polynomial of the Bloch Hamiltonian as a Laurent polynomial P_L(z, λ) = det(λI-H_B(z)) = sum_t c_t(λ) z^t , we show that the mon...