Flux insertion, entanglement, and quantized responses

We discuss the construction of a ground state wavefunction on a finite ring given the ground state on a long chain. In the presence of local symmetries, we can obtain the ground state with arbitrary flux inserted through the ring. A key ingredient are the quantum numbers of the entanglement spectrum. This method 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.