TY - JOUR
T1 - Krylov complexity in a natural basis for the Schrödinger algebra
AU - Patramanis, Dimitrios
AU - Sybesma, Watse
N1 - Publisher Copyright: Copyright D. Patramanis and W. Sybesma.
PY - 2024/4
Y1 - 2024/4
N2 - 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.
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.
UR - https://www.scopus.com/pages/publications/85199804151
U2 - 10.21468/SciPostPhysCore.7.2.037
DO - 10.21468/SciPostPhysCore.7.2.037
M3 - Article
SN - 2666-9366
VL - 7
JO - SciPost Physics Core
JF - SciPost Physics Core
IS - 2
M1 - 037
ER -