Groundstate fidelity and the spin one chain

it has been recognized quite recently that the groundstate fidelity, that is, the overlap of the groundstate wavefunctions as a function of interaction strength, can be used to obtain phase boundaries and exponents \emph{without} a-priori knowledge of the order parameter. This procedure is easy to apply in a wide class of numerical algorithms based on matrix product states, of which the Density Matrix Renormalization Group (DMRG) is the most famous. I will give a brief overview of the technique, and demonstrate that the fidelity reveals \emph{all} features of the bilinear-biquadratic spin one chain, while almost certainly ruling out the appearance of a (gapped or critical) nematic phase in the vicinity of $\theta = -3\pi / 4$.