The spin-$1/2$ Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a resonating-valence-bond-like, many-variable, Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to $4\times 4^3$ and $4\times 3^3$ spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. We consider the $(\lambda ,j_2/j_1)$ parameter space, with $j_2$, $j_1$ being nearest and next-to-nearest neighbor interactions and $\lambda$ the $XXZ$ interaction anisotropy. Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies. We find clear indications of a dimer order with spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin liquid into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.

中文翻译：

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烧绿石晶格上海森堡模型的破缺对称基态

自旋——$1/2$烧绿石晶格上的海森堡模型是一个标志性的受挫三维自旋系统，具有丰富的相图。除了包含几个有序相之外，当仅存在最近邻反铁磁相互作用时，该模型还具有自旋液体基态。在这里，我们使用精确对角化和互补变分技术通过广泛的数值研究来质疑这一假设。具体来说，我们采用共振价键状、多变量、蒙特卡罗 ansatz 和卷积神经网络量子态进行（变分）计算，最多可达$4\times 4^3$ 和 $4\times 3^3$分别旋转。我们证明这些技术产生一致的结果，允许可靠地外推到热力学极限。我们认为$(\lambda ,j_2/j_1)$ 参数空间，与 $j_2$, $j_1$ 是最近和次最近的邻居交互和 $\lambda$ 这 $XXZ$相互作用各向异性。我们的主要结果是（1）确定假定的自旋液相和相邻的磁有序相之间的相变，以及（2）根据对称性破坏趋势对基态的仔细表征。我们发现了具有自发破坏的反转和旋转对称性的二聚体有序的清晰迹象，这使无特征的量子自旋液体的场景受到质疑。我们的工作展示了如何使用多变量变分技术在回答有关三维受阻量子磁体的挑战性问题方面取得进展。