Abdelshafy Mahmoud, Rigol Marcos
Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Phys Rev E. 2023 Sep;108(3-1):034126. doi: 10.1103/PhysRevE.108.034126.
We introduce a numerical linked cluster expansion for square-lattice models whose building block is an L-shape cluster. For the spin-1/2 models studied in this work, we find that this expansion exhibits a similar or better convergence of the bare sums than that of the (larger) square-shaped clusters and can be used with resummation techniques (like the site- and bond-based expansions) to obtain results at even lower temperatures. We compare the performance of weak- and strong-embedding versions of this expansion in various spin-1/2 models and show that the strong-embedding version is preferable because of its convergence properties and lower computational cost. Finally, we show that the expansion based on the L-shape cluster can be naturally used to study properties of lattice models that smoothly connect the square and triangular lattice geometries.
我们为以L形团簇为构建块的正方晶格模型引入了一种数值链接团簇展开。对于本工作中研究的自旋-1/2模型，我们发现这种展开在裸和的收敛性方面表现出与（更大的）方形团簇相似或更好的效果，并且可以与重求和技术（如基于格点和键的展开）一起使用，以在更低温度下获得结果。我们比较了这种展开的弱嵌入和强嵌入版本在各种自旋-1/2模型中的性能，并表明强嵌入版本因其收敛特性和更低的计算成本而更可取。最后，我们表明基于L形团簇的展开可以自然地用于研究平滑连接正方晶格和三角晶格几何结构的晶格模型的性质。
