Semionic resonating valence-bond states

The nature of the kagome Heisenberg antiferromagnet (HAFM) is under ongoing debate. While recent evidence points towards a Z(2) 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 Z(2)-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 Z(2) 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.