Operator size growth in Lindbladian SYK
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910568074444800 |
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| author | Liu, Jiasheng Meyer, Rene Xian, Zhuo-Yu |
| author_facet | Liu, Jiasheng Meyer, Rene Xian, Zhuo-Yu |
| contents | We investigate the growth of operator size in the Lindbladian Sachdev-Ye-Kitaev model with $q$-body interaction terms and linear jump terms at finite dissipation strength. We compute the operator size as well as its distribution numerically at finite $q$ and analytically at large $q$. With dissipative (productive) jump terms, the size converges to a value smaller (larger) than half the number of Majorana fermions. At weak dissipation, the evolution of operator size displays a quadratic-exponential-plateau behavior. The plateau value is determined by the ratios between the coupling of the interaction and the linear jump term in the large $q$ limit. The operator size distribution remains localized in the finite size region even at late times, contrasting with the unitary case. Moreover, we also derived the time-independent orthogonal basis for operator expansion which exhibits the operator size concentration at finite dissipation. Finally, we observe that the uncertainty relation for operator size growth is saturated at large $q$, leading to classical dynamics of the operator size growth with dissipation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07115 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operator size growth in Lindbladian SYK Liu, Jiasheng Meyer, Rene Xian, Zhuo-Yu High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons Quantum Physics We investigate the growth of operator size in the Lindbladian Sachdev-Ye-Kitaev model with $q$-body interaction terms and linear jump terms at finite dissipation strength. We compute the operator size as well as its distribution numerically at finite $q$ and analytically at large $q$. With dissipative (productive) jump terms, the size converges to a value smaller (larger) than half the number of Majorana fermions. At weak dissipation, the evolution of operator size displays a quadratic-exponential-plateau behavior. The plateau value is determined by the ratios between the coupling of the interaction and the linear jump term in the large $q$ limit. The operator size distribution remains localized in the finite size region even at late times, contrasting with the unitary case. Moreover, we also derived the time-independent orthogonal basis for operator expansion which exhibits the operator size concentration at finite dissipation. Finally, we observe that the uncertainty relation for operator size growth is saturated at large $q$, leading to classical dynamics of the operator size growth with dissipation. |
| title | Operator size growth in Lindbladian SYK |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2403.07115 |