Bhattacharjee, B and Nandy, P and Pathak, T (2024) Operator dynamics in Lindbladian SYK: a Krylov complexity perspective. In: Journal of High Energy Physics, 2024 (1).
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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).
| Item Type: | Journal Article |
|---|---|
| Publication: | Journal of High Energy Physics |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to Author. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Centre for High Energy Physics |
| Date Deposited: | 01 Mar 2024 06:13 |
| Last Modified: | 01 Mar 2024 06:13 |
| URI: | https://eprints.iisc.ac.in/id/eprint/83962 |
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