Matrix Product States for Quantum Many-Fermion Systems

We describe a simple method to find the ground state energy without calculating the expectation value of the Hamiltonian in the time-evolving block decimation algorithm with tensor network states. For example, we consider quantum many-fermion systems with matrix product states, which are updated consistently in a way that accounts for fermion exchange effects. This method can be applied to a wide class of fermion systems. We test this method in spinless fermion system where the exact ground state energy is known. We analyze finite size effects to determine the ground state energy in the thermodynamic limit that is compared to the exact value.