The nature of the kagome Heisenberg antiferromagnet (HAFM) is under ongoing debate. While recent evidence points towards a
Z2 topological spin liquid, the exact nature of the topological phase is still unclear. In this paper, we introduce semionic resonating valence-bond (RVB) states, this is, resonating valence-bond states which are in the
Z2-ordered double-semion phase, and study them using projected entangled pair states. We investigate their physics and study their suitability as an ansatz for the HAFM, as compared to a conventional RVB state which is in the toric-code
Z2 topological phase. In particular, we find that a suitably optimized ``semionic simplex RVB'' outperforms the equally optimized conventional ``simplex RVB'' state, and that the entanglement spectrum (ES) of the semionic RVB behaves very differently from the ES of the conventional RVB, which suggests using the ES to discriminate the two phases. Finally, we also discuss the possible relevance of space-group symmetry breaking in valence-bond wave functions with double-semion topological order.
We have calculated the energy of the resonating-valence-bond (RVB) state made of nearest-neighbor singlet pairs in the two-dimensional Hubbard model at half filling and the energy of holes in the RVB state near half filling. The energy of the RVB state was obtained by extrapolating the result in a 6\ifmmode\times\else\texttimes\fi{}6 square lattice with the periodic boundary condition to the infinite lattice. The energy of holes was obtained by examining the first five moments of the density of states of holes in the RVB state. We find that the holes are more stabilized in the RVB state than in the N\'eel state for J/t\ensuremath{\gtrsim}0.1, where J and t are the exchange interaction and the nearest-neighbor hopping integral, respectively. We discuss the possibility of the RVB state in the high-
Tc Cu oxides.