  We show how entanglement entropies allow for the estimation of
quasi-long-range order in one dimensional systems whose low-energy physics is
well captured by the Tomonaga-Luttinger liquid universality class. First, we
check our procedure in the exactly solvable XXZ spin-1/2 chain in its entire
critical region, finding very good agreement with Bethe ansatz results. Then,
we show how phase transitions between different dominant orders may be
efficiently estimated by considering the superfluid-charge density wave
transition in a system of dipolar bosons. Finally, we discuss the application
of this method to multispecies systems such as the one dimensional Hubbard
model. Our work represent the first proof of a direct relationship between the
Luttinger parameter and R\'enyi entropies in both bosonics and fermionic
lattice models.
