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arXiv · 2409.11655

Hydrodynamic modes and operator spreading in a long-range center-of-mass-conserving Brownian SYK model

Bai-Lin Cheng·Shao-Kai Jian·Zhi-Cheng Yang
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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.

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Bai-Lin Cheng, Shao-Kai Jian, Zhi-Cheng Yang. 2024-09-18. Hydrodynamic modes and operator spreading in a long-range center-of-mass-conserving Brownian SYK model. https://arxiv.org/abs/2409.11655

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