  Finite-size scaling analysis turns out to be a powerful tool to calculate the
phase diagram as well as the critical properties of two dimensional classical
statistical mechanics models and quantum Hamiltonians in one dimension. The
most used method to locate quantum critical points is the so called crossing
method, where the estimates are obtained by comparing the mass gaps of two
distinct lattice sizes. The success of this method is due to its simplicity and
the ability to provide accurate results even considering relatively small
lattice sizes. In this paper, we introduce an estimator that locates quantum
critical points by exploring the known distinct behavior of the entanglement
entropy in critical and non critical systems. As a benchmark test, we use this
new estimator to locate the critical point of the quantum Ising chain and the
critical line of the spin-1 Blume-Capel quantum chain. The tricritical point of
this last model is also obtained. Comparison with the standard crossing method
is also presented. The method we propose is simple to implement in practice,
particularly in density matrix renormalization group calculations, and provides
us, like the crossing method, amazingly accurate results for quite small
lattice sizes. Our applications show that the proposed method has several
advantages, as compared with the standard crossing method, and we believe it
will become popular in future numerical studies.
