  We calculate the half-chain entanglement entropy of the ground state in the
one-dimensional spinless fermion model. Considering a tiny corner of the
Hilbert space represented by matrix product states, we efficiently find the
ground state by the infinite time-evolving block decimation. The Schmidt
coefficients are used to determine the half-chain entanglement entropy. Using
the bond dimension scaling of the half-chain entanglement entropy, we find the
critical region, which is consistent with the previous results.
