Krylov complexity in a natural basis for the Schrödinger algebra

gives new explicit calculations of Krylov complexities by exploiting a symmetry-based approach.

Krylov complexity is a relatively recent measure of quantum complexity, whose basic phenomenology is being actively investigated. The present article adds to this field of study by extending the formalism to theories with Schrödinger group symmetry, and argue that their method more generally lets them compute Krylov complexity for symmetry groups that posses a semi-direct sum structure.

The use of the so-called “natural basis” in which the Liouvillian is penta-diagronal is a departure from the usual Krylov algorthithm, although the authors argue that the same Krylov space is still probed.

I find the results interesting and the responses and changes made in response to another referee’s comments to have improved the paper sufficiently to merit publication. Due to the somewhat limited scope of the analysis I would, however, recommend publication in SciPost Core.

Accept in alternative Journal (see Report)