A Real-Space Formulation of the Zak Phase via Weyl m-Functions
We establish a new, real-space formula for the Zak phase for one dimensional periodic Jacobi operators in terms of the Weyl $m_+$-function that does not rely on Floquet-Bloch theory. This novel representation highlights the dependence of the Zak phase on boundary terms. Moreover, we show how to recover the classical quantisation of...