Gauging the variational optimization of projected entangled-pair states
中文速览 本文的核心论点是，在使用现代梯度下降法对投射纠缠对态（PEPS）进行变分优化时，一个被忽视的严重问题源于其内在的“规范自由度”。PEPS张量网络表示并非唯一，多种不同的张量可以描述完全相同的物理态。理想情况下，计算出的物理量（如能量）应与规范选择无关。然而，实际计算中广泛采用的近似缩并算法（如边界矩阵乘积态）破坏了这种不变性，导致计算出的近似能量严重依赖于所选的规范。本文通过理论分析和数值模拟揭示，基于自动微分的优化算法会无意中利用这一数值计算的漏洞，通过改变规范而非真正改善物理态来获得人为的、不真实的低能量，最终导致优化过程不稳定甚至失败。为解决此问题，作者提出了一种“规范固定”的优化策略，将优化过程约束在一个特定的规范流形（最小正则形式流形）上。该方法通过将能量梯度投影到此流形的切空间，系统性地移除了导致不稳定的非物理规范变换分量。在Bose-Hubbard模型上的计算结果表明，该规范固定方法成功抑制了能量发散的病态行为，获得了稳健可靠的优化结果，并证明了在PEPS变分优化中，规范固定是保证结果可靠性的关键步骤。 English Research Briefing Research Briefing: Gauging the variational optimization of projected entangled-pair states 1. The Core Contribution This paper identifies and resolves a critical pathology in the modern variational optimization of Projected Entangled-Pair States (PEPS). The central thesis is that the combination of gauge freedom inherent in the PEPS tensor representation and the approximate nature of standard tensor network contraction algorithms creates a fatal vulnerability for gradient-based optimizers. These optimizers, particularly when guided by automatic differentiation, can exploit the numerical inaccuracies of the energy calculation by performing unphysical gauge transformations that artificially lower the approximate energy, driving the simulation away from the true ground state. The paper’s primary contribution is to diagnose this mechanism of failure and introduce a robust solution: a gauge-fixed manifold optimization strategy that projects out these pathological gradient components, thereby stabilizing the optimization and ensuring convergence to physically meaningful results. ...