Z2 spin liquid in S=1/2 Heisenberg model on Kagome lattice: A projective symmetry group study of Schwinger-fermion mean-field states

TL;DR

This paper classifies and identifies a specific Z2 spin liquid state as the ground state of the S=1/2 Heisenberg model on the Kagome lattice, aligning with recent numerical findings of a gapped Z2 topological order.

Contribution

It systematically classifies all possible Z2 spin liquid states on the Kagome lattice using projective symmetry group analysis and identifies the Z2[0,π]β state as the ground state.

Findings

The Z2[0,π]β state has the lowest energy among candidate spin liquids.

The identified state matches the numerically observed gapped Z2 spin liquid.

The classification includes 20 possible Schwinger-fermion mean-field states.

Abstract

With strong geometric frustration and quantum fluctuations, S=1/2 quantum Heisenberg antiferromagnets on the Kagome lattice has long been considered as an ideal platform to realize spin liquid (SL), a novel phase with no symmetry breaking and fractionalized excitations. A recent numerical study of Heisenberg S=1/2 Kagome lattice model (HKLM) show that in contrast to earlier studies, the ground state is a singlet-gapped SL with signatures of Z2 topological order. Motivated by this numerical discovery, we use projective symmetry group to classify all 20 possible Schwinger-fermion mean-field states of Z2 SLs on Kagome lattice. Among them we found only one gapped Z2 SL (which we call Z2[0,\pi]\beta state) in the neighborhood of U(1)-Dirac SL state, whose energy is found to be the lowest among many other candidate SLs including the uniform resonating-valentce-bond states. We thus propose this Z2[0,\pi]\beta state to be the numerically discovered SL ground state of HKLM.