The technique of continuous unitary transformations has recently been used to provide physical insight into a diverse array of quantum mechanical systems. However, the question of how to best numerically implement the flow equations has received little attention. The most immediately apparent approach, using standard Runge-Kutta numerical integration algorithms, suffers from both severe inefficiency due to stiffness and the loss of unitarity. After reviewing the formalism of continuous unitary transformations and Wegner's original choice for the infinitesimal generator of the flow, we present a number of approaches to resolving these issues including a choice of generator which induces what we call the “uniform tangent decay flow” and three numerical integrators specifically designed to perform continuous unitary transformations efficiently while preserving the unitarity of flow. We conclude by applying one of the flow algorithms to a simple calculation that visually demonstrates the many-body localization transition.

中文翻译：

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稳定的ary积分器，用于连续unit变换的数值实现

连续unit变换的技术最近已用于提供对各种量子力学系统的物理了解。然而，如何最好地数字地实现流动方程的问题很少受到关注。使用标准的Runge-Kutta数值积分算法，最直接的方法就是由于刚度和单一性的丧失而导致效率低下。在回顾了连续unit变换的形式主义和Wegner对于流的无穷小生成器的最初选择之后，我们提出了许多解决这些问题的方法，包括选择产生“均匀切线衰减流”的生成器，以及专门设计用于在保持流的统一性的同时有效地执行连续three变换的三个数值积分器。我们通过将一种流量算法应用于一个简单的计算得出结论，该计算直观地演示了多体定位过渡。