Weber Manuel, Assaad Fakher F, Hohenadler Martin
Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany.
Phys Rev Lett. 2017 Sep 1;119(9):097401. doi: 10.1103/PhysRevLett.119.097401. Epub 2017 Aug 31.
The directed-loop quantum Monte Carlo method is generalized to the case of retarded interactions. Using the path integral, fermion-boson or spin-boson models are mapped to actions with retarded interactions by analytically integrating out the bosons. This yields an exact algorithm that combines the highly efficient loop updates available in the stochastic series expansion representation with the advantages of avoiding a direct sampling of the bosons. The application to electron-phonon models reveals that the method overcomes the previously detrimental issues of long autocorrelation times and exponentially decreasing acceptance rates. For example, the resulting dramatic speedup allows us to investigate the Peierls quantum phase transition on chains of up to 1282 sites.
有向回路量子蒙特卡罗方法被推广到延迟相互作用的情况。利用路径积分，通过对玻色子进行解析积分，将费米子-玻色子或自旋-玻色子模型映射到具有延迟相互作用的作用量上。这产生了一种精确算法，该算法将随机级数展开表示中可用的高效回路更新与避免直接对玻色子进行采样的优点相结合。应用于电子-声子模型表明，该方法克服了先前存在的长自相关时间和接受率呈指数下降等不利问题。例如，由此产生的显著加速使我们能够研究多达1282个格点的链上的派尔斯量子相变。
