Semionic resonating valence bond states

TL;DR

This paper introduces semionic RVB states in the Z_2 double-semion phase, compares them to conventional RVB states, and demonstrates their potential as better ansatz for the kagome Heisenberg antiferromagnet, highlighting differences in entanglement spectra.

Contribution

It presents semionic RVB states in the double-semion phase, showing they outperform conventional RVB states as ansatz for the kagome HAFM and analyzing their entanglement spectra.

Findings

Semionic RVB states outperform conventional RVB states as ansatz for HAFM.

Entanglement spectrum differs significantly between semionic and conventional RVB.

Space group symmetry breaking may be relevant in double-semion topological order.

Abstract

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 (PEPS). 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 to use the ES to discriminate the two phases. Finally, we also discuss the possible relevance of space group symmetry breaking in valence bond wavefunctions with double-semion topological order.