发表机构
École Polytechnique Fédérale de Lausanne (EPFL); Center for Quantum Science and Engineering, EPFL; Center for Computational Quantum Physics, Flatiron Institute; Università di Trieste（洛桑联邦理工学院; 洛桑联邦理工学院量子科学与工程中心; 平 inst 研究所计算量子物理中心; 的里雅斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出基于基础神经网络量子态的逆设计框架，通过梯度优化搜索哈密顿量耦合，发现方格上新的量子自旋液体候选模型$J_1$-$J_2$-$\delta$。
AI 中文摘要
设计具有所需性质的材料相当于求解一个逆问题：找到微观哈密顿量的耦合参数，使其基态展现出该性质。对于强关联量子系统，高效求解这一问题在很大程度上仍然难以实现。为了应对这一挑战，我们提出了一种基于基础神经网络量子态的从头算逆设计通用框架，该框架采用近期发展的一种方法，将一族哈密顿量的基态编码在一个变分波函数中。由于该拟设显式依赖于耦合参数，任何目标性质都是这些参数的可微函数，因此寻找正确的哈密顿量可归结为在耦合空间中进行基于梯度的优化。我们将此方法应用于搜索方格上具有不断增加的自由次近邻耦合的受抑海森堡模型的非磁性相，旨在识别新的量子自旋液体候选材料。在单个耦合的情况下，该方法恢复了方格$J_1$-$J_2$海森堡模型的已知非磁性窗口，而让两个对角耦合独立变化则揭示了一个连接方格和各向异性三角晶格区域的扩展非磁性区域。在一个包含$2\times2$单胞内八个独立耦合的搜索空间中，该空间包含若干典型的受抑自旋模型，优化自发收敛到$J_1$-$J_2$-$\delta$海森堡模型，其中对角耦合在相邻格子间交替取两个值，该模型最近在交错磁性背景下被提出。在此最优模型中对高达$16\times16$团簇进行有限尺寸标度表明，基态没有磁性、二聚体或方格子序，从而确立其为一种新的量子自旋液体候选材料，不同于先前在方格上提出的候选材料。
英文摘要
Designing a material with a desired property amounts to solving an inverse problem: finding the couplings of a microscopic Hamiltonian whose ground state exhibits that property. For strongly correlated quantum systems, solving this problem efficiently remains largely out of reach. To address this challenge, we present a general framework for ab initio inverse design based on Foundation Neural-Network Quantum States, a recent approach in which the ground states of a family of Hamiltonians are encoded in a single variational wave function. Because the ansatz depends explicitly on the couplings, any target property is a differentiable function of them, and the search for the right Hamiltonian reduces to gradient-based optimization in coupling space. We apply this approach to search for nonmagnetic phases of frustrated Heisenberg models on the square lattice with an increasing number of free next-nearest-neighbor couplings, aiming to identify new quantum spin liquid candidates. With a single coupling, the method recovers the known nonmagnetic window of the square $J_1$-$J_2$ Heisenberg model, whereas letting the two diagonal couplings vary independently reveals an extended nonmagnetic region connecting the square-lattice and anisotropic-triangular-lattice regimes. In a search space of eight independent couplings within a $2\times2$ unit cell, which contains several paradigmatic frustrated spin models, the optimization spontaneously converges to the $J_1$-$J_2$-$δ$ Heisenberg model, in which the diagonal couplings alternate between two values on neighboring plaquettes, a model recently proposed in the context of altermagnetism. Finite-size scaling up to $16\times16$ clusters in this optimal model shows that the ground state has no magnetic, dimer, or plaquette order, establishing it as a new quantum spin liquid candidate, distinct from those previously proposed on the square lattice.
Comments10 pages, 4 figures
