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Operator dynamics in Lindbladian SYK: a Krylov complexity perspectiveHighly Cited Paper

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Title
Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
Author(s)
Budhaditya Bhattacharjee; Nandy, Pratik; Pathak, Tanay
Publication Date
2024-01
Journal
Journal of High Energy Physics, v.2024, no.1
Publisher
Springer Verlag
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. © 2024, The Author(s).
URI
https://pr.ibs.re.kr/handle/8788114/15066
DOI
10.1007/JHEP01(2024)094
ISSN
1126-6708
Appears in Collections:
Center for Theoretical Physics of Complex Systems(복잡계 이론물리 연구단) > 1. Journal Papers (저널논문)
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