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Krylov complexity in a natural basis for the Schrödinger algebra
by Dimitrios Patramanis, Watse Sybesma
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Submission summary
| Authors (as registered SciPost users): | Watse Sybesma |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2306.03133v3 (pdf) |
| Date submitted: | 2023-10-25 11:21 |
| Submitted by: | Sybesma, Watse |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We investigate operator growth in quantum systems with two-dimensional Schr\"odinger group symmetry by studying the Krylov complexity. While feasible for semisimple Lie algebras, cases such as the Schr\"odinger 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.
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I thank the authors for the detailed clarifications. Before recommending the manuscript for publication in SciPost, I would suggest that the authors add these clarifications to the actual manuscript. This would make their work much more valuable to future readers.