Numerical estimation of critical parameters using the Bond entropy

Using a model of spinless fermions in a lattice with nearest neighbor and next-nearest neighbor interaction we show that the entropy of the reduced two site density matrix (the bond entropy) can be used as an extremely accurate and easy to calculate numerical indicator for the critical parameters of the quantum phase transition when the basic ordering pattern has a two-site periodicity. The actual behavior of the bond entropy depends on the particular characteristics of the transition under study. For the Kosterlitz-Thouless type phase transition from a Luttinger liquid phase to a charge density wave state the bond entropy has a local maximum while in the transition from the Luttinger liquid to the phase separated state the derivative of the bond entropy has a divergence due to the cancelation of the third eigenvalue of the two-site reduced density matrix.