With rapid progress in simulation of strongly interacting quantum Hamiltonians, the challenge in characterizing unknown phases becomes a bottleneck for scientific progress. We demonstrate that a Quantum-Classical hybrid approach (QuCl) of mining sampled projective snapshots with interpretable classical machine learning can unveil signatures of seemingly featureless quantum states. The Kitaev-Heisenberg model on a honeycomb lattice under external magnetic field presents an ideal system to test QuCl, where simulations have found an intermediate gapless phase (IGP) sandwiched between known phases, launching a debate over its elusive nature. We use the correlator convolutional neural network, trained on labeled projective snapshots, in conjunction with regularization path analysis to identify signatures of phases. We show that QuCl reproduces known features of established phases. Significantly, we also identify a signature of the IGP in the spin channel perpendicular to the field direction, which we interpret as a signature of Friedel oscillations of gapless spinons forming a Fermi surface. Our predictions can guide future experimental searches for spin liquids.

翻译：随着强相互作用量子哈密顿量模拟的快速发展，表征未知相位所面临的挑战已成为科学进步的主要瓶颈。我们证明，一种量子-经典混合方法（QuCl）通过结合可解释的经典机器学习技术对采样投影快照进行挖掘，能够揭示看似无特征的量子态的特征信号。在外加磁场作用下的蜂窝晶格基塔耶夫-海森堡模型为检验QuCl提供了理想系统——模拟结果发现已知相位之间存在一个中间无间隙相（IGP），从而引发了关于其难以捉摸本质的争论。我们采用基于标记投影快照训练的关联卷积神经网络，并结合正则化路径分析来识别不同相位的特征信号。研究表明，QuCl能够复现已知相位的已有特征。更重要的是，我们还识别出垂直于磁场方向的自旋通道中IGP的特征信号，并将其解释为形成费米面的无间隙自旋子所产生的弗里德尔振荡特征。这一预测可为未来自旋液体的实验探索提供指导。