From Dual Unitarity to Generic Quantum Operator Spreading

TL;DR

This paper explores how slight deviations from dual-unitarity in quantum circuits lead to more generic, ergodic behavior, including a butterfly velocity less than the light-cone velocity and diffusive operator spreading.

Contribution

It introduces a discrete path-integral formula for the out-of-time-order correlator to analyze the effects of weakly broken dual-unitarity on operator spreading.

Findings

Butterfly velocity is smaller than the light-cone velocity.

Operator front broadens diffusively.

Operator entanglement influences spreading dynamics.

Abstract

Dual-unitary circuits are paradigmatic examples of exactly solvable yet chaotic quantum many-body systems, but solvability naturally goes along with a degree of non-generic behaviour. By investigating the effect of weakly broken dual-unitarity on the spreading of local operators we study whether, and how, small deviations from dual-unitarity recover fully generic many-body dynamics. We present a discrete path-integral formula for the out-of-time-order correlator and use it to recover a butterfly velocity smaller than the light-cone velocity, $v_B < v_{LC}$ , and a diffusively broadening operator front, two generic features of ergodic quantum spin chains absent in dual-unitary circuit dynamics. We find that the butterfly velocity and diffusion constant are determined by a small set of microscopic quantities and that the operator entanglement of the gates plays a crucial role.