From Dual Unitarity to Generic Quantum Operator Spreading

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.

(6+15) pages, 5 figures; Accepted version; corrected some typos in the supplementary material

References in corpus (9)

• Thermalization and its mechanism for generic isolated quantum systems
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Random Quantum Circuits
• Measurement of many-body chaos using a quantum clock
• Scrambling in Random Unitary Circuits: Exact Results
• Exact dynamics in dual-unitary quantum circuits with projective measurements
• Two-step phantom relaxation of out-of-time-ordered correlations in random circuits
• Dual unitary circuits in random geometries
• Tri-unitary quantum circuits

Cited by in corpus (21)

• Majorana Loop Models for Measurement-Only Quantum Circuits
• Hierarchical generalization of dual unitarity
• Quantum information spreading in generalised dual-unitary circuits
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• The entanglement membrane in exactly solvable lattice models
• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
• Exactly solvable many-body dynamics from space-time duality
• Operator dynamics and entanglement in space-time dual Hadamard lattices
• Operator dynamics in Floquet many-body systems
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Fundamental charges for dual-unitary circuits
• Localization and integrability breaking in weakly interacting Floquet circuits
• Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points
• Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
• Exact results on the dynamics of the stochastic Floquet-East model
• Structural Stability Hypothesis of Dual Unitary Quantum Chaos
• Entanglement in dual unitary quantum circuits with impurities
• Solvable Quantum Circuits in Tree+1 Dimensions
• More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking
• Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits