We develop a formalism for constructing particle-number-conserving Gaussian fermionic projected entangled pair states [U(1)-GfPEPS] and show that these states can describe ground states of band insulators and gapless fermions with band touching points. When using them as variational Ans\"{a}tze for two Dirac fermion systems (π-flux model on the square lattice and [0,π]-flux model on the kagome lattice), we find that the U(1)-GfPEPS, even with a relatively small bond dimension, can accurately approximate the Dirac Fermi sea ground states. By applying Gutzwiller projectors on top of these U(1)-GfPEPS, we obtain PEPS representation of U(1)-Dirac spin liquid states for spin-1/2 systems. With state-of-the-art tensor network numerics, the critical exponent in the spin-spin correlation function of the Gutzwiller-projected π-flux state is estimated to be η≈1.7.
@article{arxiv.2208.04623,
title = {U(1)-symmetric Gaussian fermionic projected entangled paired states and their Gutzwiller projection},
author = {Jheng-Wei Li and Jan von Delft and Hong-Hao Tu},
journal= {arXiv preprint arXiv:2208.04623},
year = {2023}
}