Continuous matrix product states solution for the mixing/demixing transition in one-dimensional quantum fields

We solve the mixing-demixing transition in repulsive one-dimensional bose-bose mixtures. This is done numerically by means of the continuous matrix product states variational ansatz. We show that the effective low-energy bosonization theory is able to detect the transition whenever the Luttinger parameters are exactly computed. We further characterize the transition by calculating the ground-state energy density, the field-field fluctuations and the density correlations.