From Dual Unitarity to Generic Quantum Operator Spreading

• URL: http://arxiv.org/abs/2210.13490v3
• Date: Wed, 3 May 2023 14:51:30 GMT
• Title: From Dual Unitarity to Generic Quantum Operator Spreading
• Authors: Michael A. Rampp, Roderich Moessner, and Pieter W. Claeys
• Abstract summary: We study the effect of weakly broken dual-unitarity on the spreading of local operators. We find that the butterfly velocity and diffusion constant are determined by a small set of microscopic quantities.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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