论文标题
有效且灵活的方法，以模拟具有较大局部希尔伯特空间的低维量子晶格模型
Efficient and Flexible Approach to Simulate Low-Dimensional Quantum Lattice Models with Large Local Hilbert Spaces
论文作者
论文摘要
量子晶格模型在量子多体物理学的各个领域都出现了巨大的局部希尔伯特空间。诸如费米和声子之间的相互作用，相互作用的玻色子的BCS-BEC交叉或量子模拟器中的脱谐性已经在理论上和实验上进行了广泛的研究。近年来，张量网络方法已成为以数值处理晶格系统的最成功的工具之一。然而，拥有庞大的当地希尔伯特空间的系统仍然具有挑战性。在这里，我们介绍了一个映射，允许为任何类型的晶格模型构建人工$ u（1）$对称。利用产生的对称性，与本地自由度相关的数值费用显着降低。这允许对具有较大局部尺寸的系统进行有效的处理。进一步探索了该映射，我们揭示了相应矩阵 - 产品态表示的Schmidt值与单位点还原密度矩阵之间的紧密联系。我们的发现激发了典型算法中发生的截断的直观物理图片，与不利用这种人工对称性的标准方法相比，我们对数值复杂性的界限。我们演示了这个新的映射，为现有代码提供了实施配方，并在半填充时对荷斯坦模型进行示例计算。我们研究了大量的晶格站点最多$ l = 501 $的系统，同时考虑$ n _ {\ rm pH} = 63 $每个站点的$ n _ {\ rm ph} = 63 $，在CDW阶段中具有很高的精度。
Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial $U(1)$ symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrix-product-state representation and the single-site reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to $L=501$ while accounting for $N_{\rm ph}=63$ phonons per site with high precision in the CDW phase.
