The bulk-edge correspondence for topological quantum liquids states that the
spectrum of the reduced density matrix of a large subregion reproduces the
thermal spectrum of a physical edge. This correspondence suggests an intricate
connection between ground state entanglement and physical edge dynamics. We
give a simple geometric proof of the bulk-edge correspondence for a wide
variety of physical systems. Our unified proof relies on geometric techniques
available in Lorentz invariant and conformally invariant quantum field
theories. These methods were originally developed in part to understand the
physics of black holes, and we now apply them to determine the local structure
of entanglement in quantum many-body systems.Comment: 7 pages, 3 figure
