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Area of Science:

  • Quantum Many-Body Physics
  • Quantum Chaos
  • Statistical Mechanics

Background:

  • Dual-unitary circuits offer exact solvability but exhibit non-generic dynamics.
  • Understanding deviations from dual unitarity is key to exploring generic quantum many-body behavior.

Purpose of the Study:

  • To investigate how small perturbations to dual unitarity affect local operator spreading.
  • To determine if broken dual unitarity recovers generic ergodic dynamics in quantum spin chains.

Main Methods:

  • Developing a discrete path-integral formula for out-of-time-order correlators.
  • Analyzing the butterfly velocity and operator front broadening.

Main Results:

  • Recovered a butterfly velocity (vB) smaller than the light-cone velocity (vLC).
  • Observed a diffusively broadening operator front, characteristic of ergodic systems.
  • Found that butterfly velocity and diffusion constant depend on microscopic quantities and gate operator entanglement.

Conclusions:

  • Weakly broken dual unitarity restores generic, ergodic quantum many-body dynamics.
  • Operator entanglement plays a critical role in the recovery of these dynamics.
  • The findings provide insights into the transition from solvable to chaotic quantum systems.