Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet

TL;DR

This study uses variational Monte Carlo to analyze Z2 and U(1) spin liquid states on the kagome lattice, finding the U(1) Dirac state to be the most stable, aligning with recent DMRG results.

Contribution

It provides a comprehensive variational analysis of Z2 and U(1) spin liquids on the kagome lattice, demonstrating the stability of the U(1) Dirac state.

Findings

U(1) Dirac state is most stable among candidates.

Z2 states, including Z2[0,π]β, are less stable.

Adding second-neighbor exchange does not alter the U(1) Dirac ground state.

Abstract

Motivated by recent density-matrix renormalization group (DMRG) calculations [Yan, Huse, and White, Science 332, 1173 (2011)], which claimed that the ground state of the nearest-neighbor spin-1/2 Heisenberg antiferromagnet on the kagome lattice geometry is a fully gapped spin liquid with numerical signatures of Z2 gauge structure, and a further theoretical work [Lu, Ran, and Lee, Phys. Rev. B 83, 224413 (2011)], which gave a classification of all Schwinger-fermion mean-field fully symmetric Z2 spin liquids on the kagome lattice, we have thoroughly studied Gutzwiller-projected fermionic wave functions by using quantum variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. In particular, we investigated the energetics of all Z2 candidates (gapped and gapless) that lie in the neighborhood of the energetically competitive U(1) gapless spin liquids. By using a state-of-the-art optimization method, we were able to conclusively show that the U(1) Dirac state is remarkably stable with respect to all Z2 spin liquids in its neighborhood, and in particular for opening a gap toward the so-called Z2[0,{\pi}]{\beta} state, which was conjectured to describe the ground state obtained by the DMRG method. Finally, we also considered the addition of a small second nearest-neighbor exchange coupling of both antiferromagnetic and ferromagnetic type, and obtained similar results, namely, a U(1) Dirac spin-liquid ground state.