Distinguishing phases with ansatz wave functions

We propose an indistinguishability measure for assessment of ansatz wavefunctions with numerically determined wavefunctions. The measure efficiently compares all correlation functions of two states and can therefore be used to distinguish phases by defining correlator classes for ansatz wavefunctions. It also allows identification of quantum critical points. We demonstrate the approach for the transverse Ising and bilinear-biquadratic Heisenberg models, using the matrix product state formalism with the time evolving block decimation algorithm.