U(1)-symmetric Gaussian fermionic projected entangled paired states and their Gutzwiller projection

TL;DR

This paper introduces a formalism for constructing U(1)-symmetric Gaussian fermionic PEPS that effectively describe band insulators, gapless fermions, and Dirac spin liquids, with accurate approximations and critical exponent estimates.

Contribution

It develops a novel U(1)-symmetric Gaussian fermionic PEPS formalism and demonstrates their effectiveness in modeling various fermionic and spin liquid states.

Findings

U(1)-GfPEPS accurately approximate Dirac Fermi sea ground states.

Gutzwiller projection yields PEPS for U(1)-Dirac spin liquids.

Critical exponent in spin-spin correlations estimated as η ≈ 1.7.

Abstract

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 ($\pi$-flux model on the square lattice and $[0,\pi]$-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 $\pi$-flux state is estimated to be $\eta \approx 1.7$.