TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.7.2.037
TI  - Krylov complexity in a natural basis for the Schrödinger algebra
PY  - 2024/06/20
UR  - https://www.scipost.org/SciPostPhysCore.7.2.037
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 7
IS  - 2
SP  - 037
A1  - Patramanis, Dimitrios
AU  - Sybesma, Watse
AB  - We investigate operator growth in quantum systems with two-dimensional Schrödinger group symmetry by studying the Krylov complexity. While feasible for semisimple Lie algebras, cases such as the Schrödinger algebra which is characterized by a semi-direct sum structure are complicated. We propose to compute Krylov complexity for this algebra in a natural orthonormal basis, which produces a pentadiagonal structure of the time evolution operator, contrasting the usual tridiagonal Lanczos algorithm outcome. The resulting complexity behaves as expected. We advocate that this approach can provide insights to other non-semisimple algebras.
ER  -

@Article{10.21468/SciPostPhysCore.7.2.037,
	title={{Krylov complexity in a natural basis for the Schrödinger algebra}},
	author={Dimitrios Patramanis and Watse Sybesma},
	journal={SciPost Phys. Core},
	volume={7},
	pages={037},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.7.2.037},
	url={https://scipost.org/10.21468/SciPostPhysCore.7.2.037},
}