{"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}
引用次数: 0
Abstract
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.