标题： 对路径积分蒙特卡罗中分子旋转作用的近似对 显示英文标题

标题： Pair Approximating the Action For Molecular Rotations in Path Integral Monte Carlo

摘要： 典型的路径积分蒙特卡罗方法使用原始近似来计算给定路径的概率密度。 在本工作中，我们开发了配对离散变量表示（配对-DVR）方法来研究分子旋转。 最初用于研究凝聚态氦中的超流性的配对传播子，对于具有成对势的系统来说，自然非常适合。 因此，对于这样的系统，使用配对作用量采样的路径比原始 Trotter 路径更接近精确路径，从而在较少的虚时步数下实现收敛。 因此，我们的方法结合配对因子分解方法和离散化的路径积分基态（PIGS）范式来研究一个由平面转子组成的链，这些转子之间存在成对的偶极相互作用。 我们首先使用 Wigner-Kirkwood 密度展开来分析配对传播子在虚时中的渐进行为。 然后，通过比较配对传播子和原始传播子的收敛性研究，展示配对因子分解方案的实用性。 最后，我们计算了该系统的能量和结构特性，包括关联函数和 Binder 比率作为耦合强度的函数，以检查配对-DVR 方法在临界附近的性能。 在整个过程中，使用密度矩阵重整化群的结果进行基准测试。 显示英文摘要

摘要： Typical path integral Monte Carlo approaches use the primitive approximation to compute the probability density for a given path. In this work, we develop the pair Discrete Variable Representation (pair-DVR) approach to study molecular rotations. The pair propagator, which was initially introduced to study superfluidity in condensed Helium, is naturally well-suited for systems interacting with a pair-wise potential. Consequently, paths sampled using the pair action tend to be closer to the exact paths (compared to primitive Trotter paths) for such systems leading to convergence with less imaginary time steps. Therefore, our approach relies on using the pair factorization approach in conjunction with a discretized Path Integral Ground State (PIGS) paradigm to study a chain of planar rotors interacting with a pair-wise dipole interaction. We first use the Wigner-Kirkwood density expansion to analyze the asymptotics of the pair propagator in imaginary time. Then, we exhibit the utility of the pair factorization scheme via convergence studies comparing the pair and primitive propagators. Finally, we compute energetic and structural properties of this system including the correlation function and Binder ratio as functions of the coupling strength to examine the behaviour of the pair-DVR method near criticality. Density Matrix Renormalization Group results are used for benchmarking throughout.