树上的价键量子Monte Carlo算法
Valence-Bond Quantum Monte Carlo Algorithms Defined on Trees
摘要：
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。
英文摘要：
We present a new class of algorithms for performing valence-bond quantum Monte Carlo of quantum spin models. Valence-bond quantum Monte Carlo is a T=0 Monte Carlo method based on sampling of a set of operator-strings that can be viewed as forming a tree-like structure. The algorithms presented here utilize the notion of a worm that moves up and down this tree and changes the associated operator-string. In quite general terms we derive a set of equations whose solutions correspond to a new class of algorithms. As specific examples of this class of algorithms we focus on two cases. The bouncing worm algorithm, for which updates are always accepted by allowing the worm to bounce up and down the tree and the driven worm algorithm, where a single parameter controls how far up the tree the worm reaches before turning around. The latter algorithm involves only a single bounce where the worm turns from going up the tree to going down. The presence of the control parameter necessitates the introduction of an acceptance probability for the update.
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