Luttinger liquid parameters from tensor network data

We study the XXZ Heisenberg model in a staggered magnetic field using the HOTRG tensor renormalization method. Built into the tensor representation of the XXZ model is the U(1) symmetry, which is systematically maintained at each renormalization step. We determine the phase diagram of the model from the low lying spectrum, and from the finite size dependence of the spectrum we extract scaling dimensions, which are compared to predictions of low energy field theory.