We introduce a performance-optimized method to simulate localization problems on bipartite tight-binding lattices. It combines an exact renormalization group step to reduce the sparseness of the original problem with the recursive Green’s function method. We apply this framework to investigate the critical behavior of the integer quantum Hall transition of a tight-binding Hamiltonian defined on a simple square lattice. In addition, we employ an improved scaling analysis that includes two irrelevant exponents to characterize the shift of the critical energy as well as the corrections to the dimensionless Lyapunov exponent. We compare our findings with the results of a conventional implementation of the recursive Green’s function method, and we put them into broader perspective in view of recent development in this field.

我们介绍了一种性能优化的方法来模拟二分紧密绑定晶格上的局部化问题。它通过递归格林函数方法结合了精确的重整化组步骤以减少原始问题的稀疏性。我们应用此框架来研究在简单方格上定义的紧结合哈密顿量的整数量子霍尔跃迁的临界行为。此外，我们采用了改进的比例分析，其中包括两个不相关的指数来表征临界能量的移动以及对无量纲Lyapunov指数的校正。我们将我们的发现与递归格林函数方法的常规实现结果进行比较，并考虑到该领域的最新发展，将其置于更广阔的视野中。