Z$_{2}$ spin liquid phase on the kagome lattice: a new saddle point

TL;DR

This study identifies a Z2 spin liquid phase on the kagome lattice, showing it is slightly more stable than the U(1) Dirac spin liquid and suggesting the system is near a critical point rather than a fully gapped phase.

Contribution

It provides a large-scale variational analysis revealing a Z2 spin liquid state as the most stable ansatz for the kagome antiferromagnet with both NN and NNN exchanges.

Findings

Z2 spin liquid is more stable than U(1) Dirac spin liquid.

Z2 state has a small spinon gap for J2<0.2.

The system is near a critical point rather than a deep gapped phase.

Abstract

We have performed large scale variational search for the best RVB ansatz for the spin-$\frac{1}{2}$ kagome antiferromagnet with both nearest-neighboring(NN) and next-nearest-neighboring(NNN) exchanges assuming only translational symmetry. We find the best RVB state is always fully symmetric and has an mean field ansatz that is gauge equivalent to a previous proposed Z$_{2}$ spin liquid ansatz. The Z$_{2}$ state is found to be slightly more stable than the extensively studied U(1) gapless Dirac spin liquid state in both the $J_{2}\neq0$ and the $J_{2}=0$ case and to possess a small spinon gap for $J_{2}<0.2$. The breaking of the U(1) gauge symmetry in the Z$_{2}$ state is found to increase with $J_{2}$ and to be quite substantial around $J_{2}=0.15$. However, we find the Z$_{2}$ state is always very close to the gapless U(1) Dirac spin liquid state, although they have very different RVB parameters. We argue the kagome antiferromagnet should be better understood as a near critical system, rather than a system deep inside a gapped spin liquid phase with well established Z$_{2}$ topological order.