Operator dynamics in Lindbladian SYK: a Krylov complexity perspective

Understand

We use Krylov complexity to study operator growth in the $q$-body dissipative SYK model, where the dissipation is modeled by linear and random $p$-body Lindblad operators.

• In the large $q$ limit, we analytically establish the linear growth of two sets of coefficients for any generic jump operators.
• We numerically verify this by implementing the bi-Lanczos algorithm, which transforms the Lindbladian into a pure tridiagonal form.
• We find that the Krylov complexity saturates inversely with the dissipation strength, while the dissipative timescale grows logarithmically.