Operator size growth in Lindbladian SYK
| Autor: | Liu, Jiasheng, Meyer, Rene, Xian, Zhuo-Yu |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | JHEP 08 (2024) 092 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP08(2024)092 |
| Popis: | 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. Comment: 43 pages, 14 figures, major revision, published version |
| Databáze: | arXiv |
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