Kavli Affiliate: Anton R. Akhmerov
| First 5 Authors: Isidora Araya Day, Sebastian Miles, Hugo K. Kerstens, Daniel Varjas, Anton R. Akhmerov
| Summary:
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, 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 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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