Operator dynamics in Lindbladian SYK: a Krylov complexity perspective

• DOI: 10.1007/jhep01(2024)094
• Publication Date: 2024-01-18T15:03:49Z
• Authors: Budhaditya Bhatta...; Pratik Nandy; Tanay Pathak
• Keywords: High Energy Physics - Theory; Quantum Physics; Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Field Theories in Lower Dimensions; Random Systems; FOS: Physical sciences; QC770-798; 01 natural sciences; Holography and Condensed Matter Physics (AdS/CMT); Condensed Matter - Strongly Correlated Electrons; High Energy Physics - Theory (hep-th); Nuclear and particle physics. Atomic energy. Radioactivity; 0103 physical sciences; Quantum Dissipative Systems; Quantum Physics (quant-ph); Condensed Matter - Statistical Mechanics

Abstract

We use Krylov complexity to study operator growth in the q-body dissipative Sachdev-Ye-Kitaev (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.