A detailed description is provided of a new Worm Algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general Path Integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correlations in space-time, for system sizes which are orders of magnitude larger than those accessible to conventional PIMC. We present illustrative results for the superfluid transition in bulk liquid helium-four in two and three dimensions, as well as the calculation of the chemical potential of solid helium-four.
Valence-Bond Quantum Monte Carlo Algorithms Defined on Trees
本文提出了一类新的量子自旋模型的价键量子蒙特卡罗算法。价键量子蒙特卡罗（英语：Valence-bond quantum Monte Carlo）是一种T=0的蒙特卡罗方法，它基于一组算符串的采样，可以被视为形成树状结构。这里介绍的算法利用了蠕虫的概念，它在这棵树上上下移动并改变相关的运算符字符串。在相当一般的条件下，我们推导出一组方程，其解对应于一类新的算法。作为这类算法的具体例子，我们集中在两种情况下。弹跳蠕虫算法，其更新总是通过允许蠕虫在树上上下弹跳来接受，以及驱动蠕虫算法，其中单个参数控制蠕虫在转向之前到达树的高度。后一种算法只涉及一个单一的反弹，在那里蠕虫从向上到向下。控制参数的存在需要引入更新的接受概率。
