We construct a family of simple fermionic projected entangled pair states (fPEPS) on the square lattice with bond dimension $D=3$ which are exactly hole-doped resonating valence bond (RVB) wave functions with short-range singlet bonds. Under doping the insulating RVB spin liquid evolves immediately into a superconductor with mixed $d+is$ pairing symmetry whose pair amplitude grows as the square root of the doping. The relative weight between $s$-wave and $d$-wave components can be controlled by a single variational parameter $c$. We optimize our ansatz with respect to $c$ for the frustrated $t\text{−}{J}_1\text{−}{J}_2$ model (including both nearest and next-nearest neighbor antiferromagnetic interactions $J_1$ and $J_2$, respectively) for $J_2\simeq J_1/2$ and obtain an energy very close to the infinite-PEPS state (using full update optimization and same bond dimension). The orbital symmetry of the optimized RVB superconductor has predominant $d$-wave character, although we argue a residual (complex $s$-wave) time reversal symmetry breaking component should always be present. Connections of the results to the physics of superconducting cuprates and pnictides are outlined.

• Received 1 May 2014
• Revised 13 June 2014

DOI:https://doi.org/10.1103/PhysRevB.89.241106