Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916093886464000 |
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| author | Bhattacharjee, Budhaditya Nandy, Pratik Pathak, Tanay |
| author_facet | Bhattacharjee, Budhaditya Nandy, Pratik Pathak, Tanay |
| contents | 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 $\mathfrak{q}$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00753 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Operator dynamics in Lindbladian SYK: a Krylov complexity perspective Bhattacharjee, Budhaditya Nandy, Pratik Pathak, Tanay Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory 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 $\mathfrak{q}$-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. |
| title | Operator dynamics in Lindbladian SYK: a Krylov complexity perspective |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2311.00753 |