Krylov Complexity of Supersymmetric SYK Models

Abstract

We study the effect of supersymmetry breaking on Krylov complexity in the $\mathcal{N}=2$ SYK model under irrelevant and mass deformations of the Hamiltonian. The irrelevant deformation breaks $\mathcal{N}=2$ supersymmetry down to $\mathcal{N}=1$, while the mass deformation breaks supersymmetry completely. Using Krylov subspace methods, we analyze the Lanczos sequence, Krylov dimension, complexity, and entropy of the undeformed model and both deformations at finite system size. Both deformations enlarge the Krylov space and raise the saturation complexity as the BPS degeneracy is lifted. For the system sizes explored, the irrelevant deformation drives the saturation complexity to roughly half the Krylov dimension, while the mass deformation decreases it over an intermediate range of deformation strengths as the system drifts toward integrability. These distinct behaviors reveal how the mechanism of supersymmetry breaking leaves an imprint on quantum complexity.