Codebase release 2.1 for Pymablock

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.

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Publication Details

Journal
SciPost Physics Codebases
Published
2025-02-12
DOI
https://doi.org/10.21468/scipostphyscodeb.50-r2.1
Citations
3
Primary Topic
Advanced Malware Detection Techniques
Type
article
Field-Weighted Citation Impact
4.46

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Codebase release 2.1 for Pymablock

Isidora Araya Day, Sebastian Miles, Hugo Kerstens, Dániel Varjas et al.
3 citations
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Advanced Malware Detection Techniques
4.46
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Codebase release 2.1 for Pymablock

Isidora Araya Day, Sebastian Miles, Hugo Kerstens, Dániel Varjas, Anton Akhmerov
article en
3 citations

Abstract

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.

SciPost Physics Codebases
Max Planck Institute for the Physics of Complex Systems (DE), Delft University of Technology (NL)
Deutsche Forschungsgemeinschaft, Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Openalex Percentile: Top 7%
Advanced Malware Detection Techniques
4.46
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