{"title":"长程质量中心守恒布朗 SYK 模型中的流体力学模式和算子扩散","authors":"Bai-Lin Cheng, Shao-Kai Jian, Zhi-Cheng Yang","doi":"arxiv-2409.11655","DOIUrl":null,"url":null,"abstract":"We study a center-of-mass-conserving Brownian complex Sachdev-Ye-Kitaev model\nwith long-range (power-law) interactions characterized by $1/r^\\eta$. The\nkinetic constraint and long-range interactions conspire to yield rich\nhydrodynamics associated with the conserved charge, which we reveal by\ncomputing the Schwinger-Keldysh effective action. Our result shows that charge\ntransport in this system can be subdiffusive, diffusive, or superdiffusive,\nwith the dynamical exponent controlled by $\\eta$. We further employ a doubled\nHilbert space methodology to derive an effective action for the\nout-of-time-order correlator (OTOC), from which we obtain the phase diagram\ndelineating regimes where the lightcone is linear or logarithmic. Our results\nprovide a concrete example of a quantum many-body system with kinetic\nconstraint and long-range interactions in which the emergent hydrodynamic modes\nand OTOC can be computed analytically.","PeriodicalId":501226,"journal":{"name":"arXiv - PHYS - Quantum Physics","volume":"5 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hydrodynamic modes and operator spreading in a long-range center-of-mass-conserving Brownian SYK model\",\"authors\":\"Bai-Lin Cheng, Shao-Kai Jian, Zhi-Cheng Yang\",\"doi\":\"arxiv-2409.11655\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study a center-of-mass-conserving Brownian complex Sachdev-Ye-Kitaev model\\nwith long-range (power-law) interactions characterized by $1/r^\\\\eta$. The\\nkinetic constraint and long-range interactions conspire to yield rich\\nhydrodynamics associated with the conserved charge, which we reveal by\\ncomputing the Schwinger-Keldysh effective action. Our result shows that charge\\ntransport in this system can be subdiffusive, diffusive, or superdiffusive,\\nwith the dynamical exponent controlled by $\\\\eta$. We further employ a doubled\\nHilbert space methodology to derive an effective action for the\\nout-of-time-order correlator (OTOC), from which we obtain the phase diagram\\ndelineating regimes where the lightcone is linear or logarithmic. Our results\\nprovide a concrete example of a quantum many-body system with kinetic\\nconstraint and long-range interactions in which the emergent hydrodynamic modes\\nand OTOC can be computed analytically.\",\"PeriodicalId\":501226,\"journal\":{\"name\":\"arXiv - PHYS - Quantum Physics\",\"volume\":\"5 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Quantum Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11655\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Quantum Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11655","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hydrodynamic modes and operator spreading in a long-range center-of-mass-conserving Brownian SYK model
We study a center-of-mass-conserving Brownian complex Sachdev-Ye-Kitaev model
with long-range (power-law) interactions characterized by $1/r^\eta$. The
kinetic constraint and long-range interactions conspire to yield rich
hydrodynamics associated with the conserved charge, which we reveal by
computing the Schwinger-Keldysh effective action. Our result shows that charge
transport in this system can be subdiffusive, diffusive, or superdiffusive,
with the dynamical exponent controlled by $\eta$. We further employ a doubled
Hilbert space methodology to derive an effective action for the
out-of-time-order correlator (OTOC), from which we obtain the phase diagram
delineating regimes where the lightcone is linear or logarithmic. Our results
provide a concrete example of a quantum many-body system with kinetic
constraint and long-range interactions in which the emergent hydrodynamic modes
and OTOC can be computed analytically.