TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCodeb.50
TI  - Pymablock: An algorithm and a package for quasi-degenerate perturbation theory
PY  - 2025/02/12
UR  - https://www.scipost.org/SciPostPhysCodeb.50
JF  - SciPost Physics Codebases
JA  - SciPost Phys. Codebases
SP  - 50
A1  - Araya Day, Isidora
AU  - Miles, Sebastian
AU  - Kerstens, Hugo
AU  - Varjas, Daniel
AU  - Akhmerov, Anton R.
AB  - A common technique in the study of complex quantum-mechanical systems is to reduce the number of degrees of freedom in the Hamiltonian by using quasi-degenerate perturbation theory. While the Schrieffer-Wolff transformation achieves this and constructs an effective Hamiltonian, its scaling is suboptimal, it is limited to two subspaces, and implementing it efficiently is both challenging and error-prone. We introduce an algorithm for constructing an equivalent effective Hamiltonian as well as a Python package, Pymablock, that implements it. Our algorithm combines an optimal asymptotic scaling and the ability to handle any number of subspaces with a range of other improvements. The package supports numerical and analytical calculations of any order and it is designed to be interoperable with any other packages for specifying the Hamiltonian. We demonstrate how the package handles constructing a k.p model, analyses a superconducting qubit, and computes the low-energy spectrum of a large tight-binding model. We also compare its performance with reference calculations and demonstrate its efficiency.
ER  -

@Article{10.21468/SciPostPhysCodeb.50,
	title={{Pymablock: An algorithm and a package for quasi-degenerate perturbation theory}},
	author={Isidora Araya Day and Sebastian Miles and Hugo K. Kerstens and Daniel Varjas and Anton R. Akhmerov},
	journal={SciPost Phys. Codebases},
	pages={50},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCodeb.50},
	url={https://scipost.org/10.21468/SciPostPhysCodeb.50},
}

@Article{10.21468/SciPostPhysCodeb.50-r2.1,
	title={{Codebase release 2.1 for Pymablock}},
	author={Isidora Araya Day and Sebastian Miles and Hugo K. Kerstens and Daniel Varjas and Anton R. Akhmerov},
	journal={SciPost Phys. Codebases},
	pages={50-r2.1},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCodeb.50-r2.1},
	url={https://scipost.org/10.21468/SciPostPhysCodeb.50-r2.1},
}