标题： 使用簇iTEBD方法确定一维量子系统的基态 显示英文标题

标题： Determination of ground states of one-dimensional quantum systems using the cluster iTEBD method

摘要： 在矩阵乘积态的虚时演化框架中，我们引入了一种簇版本的无限时间演化块削减算法，用于模拟量子多体系统，解决了强关联物理中的计算精度挑战。 通过重新定义波函数假设以包含多个物理自由度，我们增强了纠缠的表示，从而提高了基态的准确性。 利用Trotter-Suzuki分解和优化的截断方案，我们的方法保持了大致相同的计算复杂度，同时捕捉到更多的量子关联。 我们将这种方法应用于三个非平凡的情况：无能隙的自旋-1/2海森堡链，具有高阶高斯型相变的自旋-1各向异性XXZD链，以及一个具有磁平台相的自旋-1/2扭曲三角棱柱。 在物理量如磁化强度、基态能量和纠缠熵方面，已展示了更高的准确性。 该方法为研究具有高精度的复杂量子系统提供了一个可扩展的框架，使其适用于仅增加键维无法保证满意结果的情况。 显示英文摘要

摘要： Within the framework of imaginary-time evolution for matrix product states, we introduce a cluster version of the infinite time-evolving block decimation algorithm for simulating quantum many-body systems, addressing the computational accuracy challenges in strongly correlated physics. By redefining the wave-function ansatz to incorporate multiple physical degrees of freedom, we enhance the representation of entanglement, thereby improving the accuracy of the ground states. Utilizing the Trotter-Suzuki decomposition and optimized truncation schemes, our method maintains roughly the same computational complexity while capturing more quantum correlations. We apply this approach to three nontrivial cases: the gapless spin-1/2 Heisenberg chain, the spin-1 anisotropic XXZD chain with a higher-order Gaussian-type phase transition, and a spin-1/2 twisted triangular prism hosting a magnetic plateau phase. Improved accuracy in physical quantities, such as magnetization, ground-state energy, and entanglement entropy, has been demonstrated. This method provides a scalable framework for studying complex quantum systems with high precision, making it suitable for situations where a pure increase in bond dimension alone cannot guarantee satisfactory results.