Programme

P.9 -- Poster, ANSWCCMS-2023

Date: Tuesday, 7 November 2023

Time: 13:00 - 14:30

Operator dynamics in Lindbladian SYK: A Krylov complexity perspective

Budhaditya Bhattacharjee

Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon, Korea

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. This is akin to the behavior of other Q-complexity measures, namely out-of-time-order correlator (OTOC) and operator size, which we also demonstrate. We connect these observations to continuous quantum measurement processes. We further investigate the pole structure of a generic auto-correlation and the high-frequency behavior of the spectral function in the presence of dissipation, thereby revealing a general principle for operator growth in dissipative quantum chaotic systems.

Presenter: Budhaditya Bhattacharjee