Speaker
Description
The concept of bulk-boundary correspondence is essentially that the existence of edge states in topological insulators can be predicted from topological invariants of the bulk. The existing proofs of bulk-boundary correspondence in one dimension are usually not very physically insightful and rely on very involved mathematics. We provide a novel formulation of bulk-boundary correspondence for semi-infinite chains which relies on analytically continuing the Bloch Hamiltonian, $h(k)$ to complex wavenumbers $k$. We show that chiral symmetry results in exceptional points in the (now non-Hermitian) analytically continued $h(k)$ where two eigenstates and eigenvalues coalesce. States arising at those exceptional points are edge states of semi-infinite chains: they satisfy the boundary condition, are normalizable in semi-infinite systems and have real energy. The number of such edge states is adiabatically protected, provided chiral symmetry is not broken. Finally, we derive winding numbers, which can be interpreted as topological invariants, that quantify the number of edge states arising at exceptional points. We compare these winding numbers to the Zak phase and give the quantized Zak phase an alternative interpretation.