RVB superconductors with fermionic projected entangled pair states

TL;DR

This paper constructs a fermionic PEPS model for doped RVB states on a square lattice, revealing immediate superconductivity with mixed d+is pairing symmetry and close energy proximity to infinite-PEPS states, with implications for cuprate and pnictide superconductors.

Contribution

It introduces a simple fermionic PEPS ansatz for doped RVB states that captures superconductivity with mixed pairing symmetry and achieves near-optimal energies for the frustrated t-J model.

Findings

Doped RVB states evolve into superconductors with d+is pairing.

Pair amplitude scales with the square root of doping.

Optimized states have energies close to infinite-PEPS solutions.

Abstract

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) wavefunctions 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 w.r.t. $c$ for the frustrated $t-J_1-J_2$ 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.