SymPT: a comprehensive tool for automating effective Hamiltonian derivations

TL;DR

SymPT is an automated software tool that simplifies and generalizes the derivation of effective Hamiltonians using the Schrieffer-Wolff transformation, applicable to complex quantum systems with time-dependent or periodic Hamiltonians.

Contribution

The paper introduces SymPT, a software that automates and extends the Schrieffer-Wolff transformation for complex and time-dependent quantum systems, reducing computational effort and errors.

Findings

Automates derivation of effective Hamiltonians.

Supports time-dependent and periodic Hamiltonians.

Enables precise handling of complex energy structures.

Abstract

The Schrieffer-Wolff transformation (SWT) is a foundational perturbative method for deriving effective Hamiltonians in quantum systems by systematically eliminating couplings between pairs of energy distant subspaces. Despite recent advancements, the implementation of SWTs for sufficiently complex systems remains computationally challenging and often requires extensive calculations that are prone to errors. In this work, we introduce an analytical software tool, SymPT (Symbolic Perturbation Theory), designed to automate the SWT and its extensions. Building on a universal framework developed in recent research, SymPT provides a systematic and generalizable solution for deriving the generator of the transformation, enabling accurate computation of effective Hamiltonians for arbitrary perturbative systems. The tool supports both time-independent and time-periodic Hamiltonians, extending beyond standard SWT to incorporate arbitrary coupling elimination, block-diagonalization and full-diagonalization routines, thus enabling precise handling of systems with intricate energy structures.