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

Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law