利用神经网络量子态接近热力学极限
Approaching the Thermodynamic Limit with Neural-Network Quantum States
AI总结：
本文提出空间注意力机制，用于神经网络量子态模拟，实现了对大系统热力学极限的高精度模拟，优于张量网络方法。
摘要：
访问强关联量子物质的热力学极限性质需要在非常大的晶格上进行模拟，这一领域仍然是数值方法面临的挑战，尤其是在受挫的二维系统中。我们引入了空间注意力机制，这是一种最小且物理上可解释的归纳偏差，用于神经网络量子态，其在Transformer架构中实现为一个单一的学得长度尺度。这种偏差稳定了大规模优化，并通过在变分蒙特卡洛框架内对前所未有的系统规模进行高精度模拟，使能够访问热力学极限物理。应用于自旋-1/2三角晶格反铁磁Heisenberg模型，我们的方法在最多42×42个站点的簇上实现了最先进的结果。能够模拟如此大的系统允许对能量和序参量进行受控的有限尺寸缩放，从而提取实验相关量，如自旋波速度和均匀磁化率。反过来，我们发现外推的热力学极限能量系统比用张量网络方法如iPEPS获得的能量更系统更好。所得到的磁化率被强烈地重整化，M0=0.148(1)（约为经典值的30%），表明更不准确的变分态系统系统性地高估了磁序。对优化的波函数的分析进一步表明存在内在的非局域符号结构，表明符号问题无法通过局部基变换去除。最后，我们通过获得J1-J2 Heisenberg模型在20×20正方形晶格上的最先进能量，证明了该方法的通用性，优于残差卷积神经网络。
英文摘要：
Accessing the thermodynamic-limit properties of strongly correlated quantum matter requires simulations on very large lattices, a regime that remains challenging for numerical methods, especially in frustrated two-dimensional systems. We introduce the Spatial Attention mechanism, a minimal and physically interpretable inductive bias for Neural-Network Quantum States, implemented as a single learned length scale within the Transformer architecture. This bias stabilizes large-scale optimization and enables access to thermodynamic-limit physics through highly accurate simulations on unprecedented system sizes within the Variational Monte Carlo framework. Applied to the spin-$\tfrac12$ triangular-lattice Heisenberg antiferromagnet, our approach achieves state-of-the-art results on clusters of up to $42\times42$ sites. The ability to simulate such large systems allows controlled finite-size scaling of energies and order parameters, enabling the extraction of experimentally relevant quantities such as spin-wave velocities and uniform susceptibilities. In turn, we find extrapolated thermodynamic limit energies systematically better than those obtained with tensor-network approaches such as iPEPS. The resulting magnetization is strongly renormalized, $M_0=0.148(1)$ (about $30\%$ of the classical value), revealing that less accurate variational states systematically overestimate magnetic order. Analysis of the optimized wave function further suggests an intrinsically non-local sign structure, indicating that the sign problem cannot be removed by local basis transformations. We finally demonstrate the generality of the method by obtaining state-of-the-art energies for a $J_1$-$J_2$ Heisenberg model on a $20\times20$ square lattice, outperforming Residual Convolutional Neural Networks.
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