Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study

TL;DR

This study classifies valence-bond crystals on the kagome lattice and demonstrates the stability of the U(1) Dirac spin liquid against various valence-bond crystal formations using advanced variational Monte Carlo methods.

Contribution

It provides a comprehensive symmetry-based classification of VBCs on the kagome lattice and shows the stability of the U(1) Dirac spin liquid against dimerization.

Findings

U(1) Dirac spin liquid is stable against several VBCs.

A 36-site VBC is stabilized with small ferromagnetic next-nearest-neighbor coupling.

The 36-site VBC breaks reflection symmetry and has a nontrivial flux pattern.

Abstract

In this paper, we do a complete classification of valence-bond crystals (VBCs) on the kagome lattice based on general arguments of symmetry only and thus identify many new VBCs for different unit cell sizes. For the spin-1/2 Heisenberg antiferromagnet, we study the relative energetics of competing gapless spin liquids (SLs) and VBC phases within the class of Gutzwiller-projected fermionic wave functions using variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. By using a state-of-the-art optimization method, we conclusively show that the U(1) Dirac SL is remarkably stable towards dimerizing into all 6-, 12- and 36-site unit cell VBCs. This stability is also preserved on addition of a next-nearest-neighbor super-exchange coupling of both antiferromagnetic and ferromagnetic (FM) type. However, we find that a 36-site unit cell VBC is stabilized on addition of a very small next-nearest-neighbor FM super-exchange coupling, i.e. |J2|~0.045, and this VBC is the same in terms of space-group symmetry as that obtained in an effective quantum dimer model study. It breaks reflection symmetry, has a nontrivial flux pattern and is a strong dimerization of the uniform RVB SL.