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We numerically study the spectral properties, the entanglement and thezero-temperature phase structure at nonvanishing chemical potential of the O(3)nonlinear sigma model. Using matrix product states, a particular kind ofone-dimensional tensor network state, we show that we are able to reach theasymptotic scaling regime and to reproduce the analytical predictions for themass gap at vanishing chemical potential. In addition, we study the scaling ofthe entanglement entropy towards the continuum limit obtaining a central chargeconsistent with 2. Moreover, our approach does not suffer from the sign problemand we also explore the phase structure of the model for nonzero chemicalpotential and map out the location of the transitions between different chargesectors with high precision.

O(3) nonlinear sigma model in 1+1 dimensions with matrix product states