The recent progress in the optimization of two-dimensional tensor networks [H.-J. Liao, J.-G. Liu, L. Wang, and T. Xiang, Phys. Rev. X 9, 031041 (2019)] based on automatic differentiation opened the way towards precise and fast optimization of such states and, in particular, infinite projected entangled-pair states (iPEPS) that constitute a generic-purpose Ansatz for lattice problems governed by local Hamiltonians. In this work, we perform an extensive study of a paradigmatic model of frustrated magnetism, the J 1 − J 2 Heisenberg an- tiferromagnet on the square lattice. By using advances in both optimization and subsequent data analysis, through finite correlation-length scaling, we re- port accurate estimations of the magnetization curve in the Néel phase for J 2 /J 1 ≤ 0.45. The unrestricted iPEPS simulations reveal an U (1) symmetric structure, which we identify and impose on tensors, resulting in a clean and consistent picture of antiferromagnetic order vanishing at the phase transition with a quantum paramagnet at J 2 /J 1 ≈ 0.46(1). The present methodology can be extended beyond this model to study generic order-to-disorder transitions in magnetic systems.

中文翻译：

---

可微的对称张量网络研究沮丧的海森堡反铁磁体的Néel相

二维张量网络优化的最新进展[H.-J. 廖建国 Liu，L. Wang和T. Xiang，物理 修订版X 9，031041（2019）]基于自动微分，为精确，快速优化此类状态开辟了道路，特别是无限投影纠缠对状态（iPEPS）构成了通用Ansatz，用于解决受控制的晶格问题由当地的汉密尔顿主义者。在这项工作中，我们对沮丧的磁学模型（方格上的J 1-J 2 Heisenberg反铁磁）进行了广泛的研究。通过利用优化和后续数据分析的进步，通过有限的相关长度缩放，我们报告了J 2 / J 1≤0.45时Néel相中磁化曲线的准确估计。无限制的iPEPS模拟显示了U（1）对称结构，我们将其识别并施加在张量上，从而得到清晰一致的反铁磁阶数，并且在相变处使用量子顺磁体J 2 / J 1≈0.46（1）消失。可以将本方法学扩展到该模型之外，以研究磁性系统中一般的有序到无序过渡。