Estimating quasi-long-range order via Rényi entropies

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 represents the first proof of a direct relationship between the Luttinger parameter and R\'enyi entropies in both bosonic and fermionic lattice models.