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

TL;DR

This paper analyzes a long-range, charge-conserving Brownian SYK model, revealing how hydrodynamics and operator spreading depend on interaction range, with analytical results for different transport regimes and OTOC behavior.

Contribution

It provides the first analytical derivation of hydrodynamics and OTOC phase diagram in a long-range, constrained quantum many-body system.

Findings

Charge transport can be subdiffusive, diffusive, or superdiffusive depending on $\

The phase diagram shows regimes with linear or logarithmic lightcone behavior.

Analytical expressions for hydrodynamic modes and OTOC in a long-range SYK model.

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.