Dirac-type nodal spin liquid revealed by machine learning

Pursuing fractionalized particles that do not bear properties of conventional bare particles such as electrons or magnons is a challenge in physics. Here we show that machine-learning methods for quantum many-body systems reveal the existence of a quantum spin liquid state with fractionalized spinons in spin-1/2 frustrated Heisenberg model convincingly, if it is combined with the state-of-the-art computational schemes known as the correlation ratio and level spectroscopy methods. The spin excitation spectra signal the emergence of gapless fractionalized spin-1/2 Dirac-type spinons in the distinctive quantum spin liquid phase. Unexplored critical behavior with coexisting power-law-decaying antiferromagnetic and dimer correlations emerges as well. The isomorph of excitations with the cuprate d-wave superconductors revealed here implies tight connection between the present spin liquid and superconductivity. This achievement manifests the power of machine learning for grand challenges in quantum many-body physics.