Flux insertion, entanglement, and quantized responses

There has been much discussion about which aspects of the entanglement spectrum are in fact robust properties of a bulk phase. By making use of a trick for constructing the ground state of a system on a ring given the ground state on an infinite chain, we show why the entanglement spectrum combined with the quantum numbers of the Schmidt states encodes a variety of robust topological observables. We introduce a method that allows us to characterize phases by measuring quantized responses, such as the Hall conductance, using data contained in the entanglement spectrum. As concrete examples, we show how the Berry phase allows us to map out the phase diagram of a spin-1 model and calculate the Hall conductivity of a quantum Hall system.