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

Bai-Lin Cheng1, Shao-Kai Jian2, Zhi-Cheng Yang1,3

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We analyzed a complex quantum system with long-range interactions. Charge transport can vary from subdiffusive to superdiffusive, depending on interaction details.

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Area of Science:

  • Quantum Many-Body Physics
  • Condensed Matter Theory
  • Statistical Mechanics

Background:

  • The Sachdev-Ye-Kitaev (SYK) model is a key theoretical framework for studying quantum chaos and thermalization.
  • Understanding hydrodynamics in systems with both kinetic constraints and long-range interactions is crucial for describing emergent phenomena.

Purpose of the Study:

  • To investigate the charge transport properties of a center-of-mass-conserving Brownian complex SYK model with power-law interactions.
  • To explore the interplay between kinetic constraints and long-range interactions on system hydrodynamics.
  • To analytically derive the effective action for the out-of-time-order correlator (OTOC) and map the phase diagram.

Main Methods:

  • Schwinger-Keldysh effective action formalism to compute hydrodynamics.
  • Doubled Hilbert space methodology for deriving the effective action of the OTOC.
  • Analysis of power-law interactions characterized by 1/r^{η}.

Main Results:

  • Revealed rich hydrodynamics associated with conserved charge, showing tunable charge transport (subdiffusive, diffusive, superdiffusive) controlled by the exponent η.
  • Derived the phase diagram for the OTOC, distinguishing between linear and logarithmic light-cone propagation.
  • Provided an analytical framework for emergent hydrodynamic modes and OTOC in this complex quantum system.

Conclusions:

  • The study presents a concrete quantum many-body system with kinetic constraints and long-range interactions exhibiting tunable transport properties.
  • Analytical results for hydrodynamics and OTOC offer insights into quantum chaos and thermalization in such systems.
  • The findings bridge the gap between microscopic models and macroscopic emergent behavior in complex quantum matter.