2024/12/13 by Giovanni Francesco Diotallevi, Diotallevi, Giovanni Francesco, Leander Reascos +3
Computer Science · Mathematics · #Distributed and Parallel Computing Systems #Parallel Computing and Optimization Techniques #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2412.10240
The Schrieffer-Wolff transformation (SWT) is a foundational perturbative\nmethod for deriving effective Hamiltonians in quantum systems by systematically\neliminating couplings between pairs of energy distant subspaces. Despite recent\nadvancements, the implementation of SWTs for sufficiently complex systems\nremains computationally challenging and often requires extensive calculations\nthat are prone to errors. In this work, we introduce an analytical software\ntool, SymPT (Symbolic Perturbation Theory), designed to automate the SWT and\nits extensions. Building on a universal framework developed in recent research,\nSymPT provides a systematic and generalizable solution for deriving the\ngenerator of the transformation, enabling accurate computation of effective\nHamiltonians for arbitrary perturbative systems. The tool supports both\ntime-independent and time-periodic Hamiltonians, extending beyond standard SWT\nto incorporate arbitrary coupling elimination, block-diagonalization and\nfull-diagonalization routines, thus enabling precise handling of systems with\nintricate energy structures.\n