论文标题
通过可区分的对称张量网络对沮丧的Heisenberg Antiferromagnet的Néel阶段的调查
Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks
论文作者
论文摘要
二维张量网络优化的最新进展[H.-J. Liao，J.-G。 Liu，L。Wang和T. Xiang，物理。基于自动差异化的修订版x $ {\ bf 9} $，031041（2019）]为这些状态的精确和快速优化开辟了道路，尤其是无限投影的纠缠pair态（IPEP），该状态（ipeps）构成了一个通用的porpose $ {\ its ansatz;在这项工作中，我们对沮丧的磁性模型进行了广泛的研究，即$ J_1-J_2 $ HEISENBERG ANTIFERROMAGNET在Square Grattice上。通过在优化和后续数据分析中使用有限的相关长度缩放，我们报告了Néel相中磁化曲线的准确估计，以$ J_2/J_1 \ le 0.45 $。无限制的IPEPS模拟显示了$ U（1）$对称结构，我们将其识别并强加于张量，从而在$ j_2/j_1 $ j_2/j_1 \约0.46（1）$的量子过渡时清晰且一致地描绘了抗fiferromagnetic Order在相过渡时消失的图片。目前的方法可以扩展到该模型之外，以研究磁系统中的通用订单到二级转换。
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 ${\bf 9}$, 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 ${\it Ansatz}$ 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 antiferromagnet on the square lattice. By using advances in both optimization and subsequent data analysis, through finite correlation-length scaling, we report accurate estimations of the magnetization curve in the Néel phase for $J_2/J_1 \le 0.45$. 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 $J_2/J_1 \approx 0.46(1)$. The present methodology can be extended beyond this model to study generic order-to-disorder transitions in magnetic systems.
