标题： 简化环状玻色-哈巴德系统的高阶微扰理论 显示英文标题

标题： Simplifying higher-order perturbation theory for ring-shaped Bose-Hubbard systems

摘要： 本文中，高阶微扰理论被应用于一维环状玻色-哈伯德系统，并进行了专门调整。 光谱特性和几何特性被用来结构性地简化贡献项并减少计算工作量，同时不牺牲准确性。 为此，提供了一份计算到九阶的各个微扰阶数的指南，以及一个既与系统相关又依赖于参数设定的收敛标准。 所描述的简化方案被发现适用于具有不同晶格几何形状的一类更广泛的玻色-哈伯德系统。 通过排斥 onsite 相互作用的三站点玻色-哈伯德系统的基态能量的显式计算，包含了对此发现的一个示例验证。 这些计算成功地通过精确对角化结果的数值计算进行了验证。 显示英文摘要

摘要： In this paper, higher-order perturbation theory is applied and tailored to one-dimensional ring-shaped Bose-Hubbard systems. Spectral and geometrical properties are used to structurally simplify the contributions and reduce computational effort without sacrificing accuracy. For this, a guide for the computation of the individual perturbational orders up to order nine is provided, alongside a both system-specific and parametrization-dependent convergence criterion. The simplification scheme described is found to be applicable to a wider class of Bose-Hubbard systems with different lattice geometries. An exemplary validation of these findings is included in the form of explicit calculations of ground state energies of the three-site Bose-Hubbard system with repulsive on-site interactions. These calculations are successfully checked against numerical computations of exact diagonalization results.