  Tensor network states and parton wave functions are two pivotal methods for
studying quantum many-body systems. This work connects these two subjects as we
demonstrate that a variety of parton wave functions, such as projected Fermi
sea and projected fermionic or bosonic paired states, can be represented
exactly as tensor networks. The results can be compressed into matrix product
states with moderate bond dimensions so various physical quantities can be
computed efficiently. For the projected Fermi sea, we develop an excellent
compression scheme with high fidelity using maximally localized Wannier
orbitals. Numerical calculations on two parton wave functions demonstrate that
our method exceeds commonly adopted Monte Carlo methods in some aspects. It
produces energy and correlation function with very high accuracy that is
difficult to achieve using Monte Carlo method. The entanglement measures that
were almost impossible to compute before can also be obtained easily using our
method.
