Hydrodynamic Modes and Operator Spreading in a Long-Range Center-of-Mass-Conserving Brownian Sachdev-Ye-Kitaev Model

We study a center-of-mass-conserving Brownian complex Sachdev-Ye-Kitaev model with long-range (power-law) interactions characterized by 1/r^{η}. 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 η. We further employ a doubled Hilbert space methodology to derive an effective action for the out-of-time-order correlator, from which we obtain the phase diagram delineating regimes where the light cone 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 out-of-time-order correlator can be computed analytically.