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The technique of continuous unitary transformations has recently been used toprovide physical insight into a diverse array of quantum mechanical systems.However, the question of how to best numerically implement the flow equationshas received little attention. The most immediately apparent approach, usingstandard Runge-Kutta numerical integration algorithms, suffers from both severeinefficiency due to stiffness and the loss of unitarity. After reviewing theformalism of continuous unitary transformations and Wegner's original choicefor the infinitesimal generator of the flow, we present a number of approachesto resolving these issues including a choice of generator which induces what wecall the "uniform tangent decay flow" and three numerical integratorsspecifically designed to perform continuous unitary transformations efficientlywhile preserving the unitarity of flow. We conclude by applying one of the flowalgorithms to a simple calculation that visually demonstrates the many-bodylocalization transition.

Stable Unitary Integrators for the Numerical Implementation of Continuous Unitary Transformations