通过子空间迭代实现快速二维张量网络收缩
Fast two-dimensional tensor-network contraction via subspace iteration
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中文总结 AI 辅助
研究针对无限投影纠缠对态收缩方法计算成本高的问题，提出子空间迭代CTMRG方法，通过基于QR投影器构造，用小矩阵SVD替代大矩阵SVD，转移主要成本，适合GPU加速，在三角晶格海森堡反铁磁体计算中效率高且结果优。
中文摘要 AI 辅助
角转移矩阵重整化群（CTMRG）是无限投影纠缠对态（iPEPS）的标准收缩方法之一，但其计算成本主要由重复的截断奇异值分解（SVD）主导。我们引入了基于QR投影器构造的子空间迭代CTMRG（SI - CTMRG），用更小矩阵的SVD替代每个大矩阵SVD。该算法将主要成本从分解转移到张量收缩，非常适合GPU加速，比标准CTMRG提速高达两个数量级。我们展示了该方法对三角晶格海森堡反铁磁体的效率和准确性，在单个H100 GPU上约10小时计算就达到了当前最优的iPEPS结果。
英文摘要
The corner transfer matrix renormalization group (CTMRG) is one of the standard contraction methods for infinite projected entangled-pair states (iPEPS), but its computational cost is dominated by repeated truncated singular value decompositions (SVDs). We introduce subspace-iteration CTMRG (SI-CTMRG), a QR-based projector construction that replaces each large-matrix SVD with an SVD of a much smaller matrix. The resulting algorithm shifts the dominant cost from decompositions to tensor contractions, making it highly suited to GPU acceleration and yielding speedups of up to two orders of magnitude over standard CTMRG. We demonstrate the efficiency and accuracy of the method for the triangular-lattice Heisenberg antiferromagnet, reaching state-of-the-art iPEPS results on a single H100 GPU in approximately 10 hours of computation.
