路径积分蒙特卡洛在离散变量表示中与吉布斯采样：偶极子平面转子链
Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: dipolar planar rotor chain
AI总结：
本文提出了一种基于离散变量和吉布斯采样的路径积分蒙特卡洛方法，用于研究偶极子平面转子链的基态性质，并通过对比不同方法验证了该方法的优越性。
摘要：
在本工作中，我们提出了一种基于离散连续自由度和无拒绝吉布斯采样的路径积分蒙特卡洛（PIMC）方法。利用平面转子链的基态性质来说明该方法。计算了能量和结构性质，并与精确对角化和数值矩阵乘法对于N≤3的情况进行比较，以评估系统性 Trotter 分解误差收敛情况。对于更大的链，最多有N=100个转子，使用密度矩阵重整化群（DMRG）计算作为基准。我们展示了使用吉布斯采样比传统Metropolis-Hastings拒绝重要采样更具优势。事实上，吉布斯采样导致计算可观测量的方差和相关性较低。
英文摘要：
In this work, we propose a Path Integral Monte Carlo (PIMC) approach based on discretized continuous degrees of freedom and rejection-free Gibbs sampling. The ground state properties of a chain of planar rotors with dipole-dipole interactions are used to illustrate the approach. Energetic and structural properties are computed and compared to exact diagonalization and Numerical Matrix Multiplication for $N \leq 3$ to assess the systematic Trotter factorization error convergence. For larger chains with up to N = 100 rotors, Density Matrix Renormalization Group (DMRG) calculations are used as a benchmark. We show that using Gibbs sampling is advantageous compared to traditional Metroplolis-Hastings rejection importance sampling. Indeed, Gibbs sampling leads to lower variance and correlation in the computed observables.
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