  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.
