Persistence of the gapless spin liquid in the breathing kagome Heisenberg antiferromagnet

TL;DR

This study investigates the ground state of the breathing kagome Heisenberg antiferromagnet, finding that the gapless U(1) Dirac spin liquid remains stable and does not transition to a gapped Z2 spin liquid across various anisotropy ratios.

Contribution

The paper demonstrates that the gapped Z2 spin liquid is not energetically favored in the breathing kagome model, confirming the persistence of the gapless spin liquid state.

Findings

Gapped spin liquid energy gain vanishes in the thermodynamic limit.

Pairing amplitudes responsible for spin gap tend to zero as system size increases.

No energy improvement for gapped states with Lanczos steps.

Abstract

The nature of the ground state of the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e., with different superexchange couplings $J_{\vartriangle}$ and $J_{\triangledown}$ within elementary up- and down-pointing triangles) is investigated within the framework of Gutzwiller projected fermionic wave functions and Monte Carlo methods. We analyze the stability of the U(1) Dirac spin liquid with respect to the presence of fermionic pairing that leads to a gapped $\mathbb{Z}_{2}$ spin liquid. For several values of the ratio $J_{\triangledown}/J_{\vartriangle}$, the size scaling of the energy gain due to the pairing fields and the variational parameters are reported. Our results show that the energy gain of the gapped spin liquid with respect to the gapless state either vanishes for large enough system size or scales to zero in the thermodynamic limit. Similarly, the optimized pairing amplitudes (responsible for opening the spin gap) are shown to vanish in the thermodynamic limit. Our outcome is corroborated by the application of one and two Lanczos steps to the gapless and gapped wave functions, for which no energy gain of the gapped state is detected when improving the quality of the variational states. Finally, we discuss the competition with the "simplex" $\mathbb{Z}_{2}$ resonating-valence-bond spin liquid, valence-bond crystal, and nematic states in the strongly anisotropic regime, i.e., $J_{\triangledown} \ll J_{\vartriangle}$.