From Dual Unitarity to Generic Quantum Operator Spreading
arXiv:2210.13490 · doi:10.1103/PhysRevLett.130.130402
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, , 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.
arXiv comment(6+15) pages, 5 figures; Accepted version; corrected some typos in the supplementary material
References in corpus (46)
- Thermalization and its mechanism for generic isolated quantum systems
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Operator Spreading in Random Unitary Circuits
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
- Measuring the scrambling of quantum information
- Random Quantum Circuits
- A Universal Operator Growth Hypothesis
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- Information Scrambling in Computationally Complex Quantum Circuits
- Entanglement of Quantum Evolutions
- Solution of a minimal model for many-body quantum chaos
- Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
- Exact dynamics in dual-unitary quantum circuits
- Entanglement spreading in a minimal model of maximal many-body quantum chaos
- Unitary circuits of finite depth and infinite width from quantum channels
- Dark Radiation and Superheavy Dark Matter from Black Hole Domination
- Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
- Measurement of many-body chaos using a quantum clock
- The entanglement membrane in chaotic many-body systems
- Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
- Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
- Scrambling in Random Unitary Circuits: Exact Results
- Locality, Quantum Fluctuations, and Scrambling
- Exact emergent quantum state designs from quantum chaotic dynamics
- Particle-Time Duality in the Kicked Ising Chain I: The Dual Operator
- Particle-Time Duality in the Kicked Ising Chain II: Applications to the Spectrum
- Accessing scrambling using matrix product operators
- Probing scrambling using statistical correlations between randomized measurements
- Maximum velocity quantum circuits
- Influence matrix approach to many-body Floquet dynamics
- From dual-unitary to quantum Bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy
- Creating ensembles of dual unitary and maximally entangling quantum evolutions
- Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits
- Computational power of one- and two-dimensional dual-unitary quantum circuits
- Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
- Maximal entanglement velocity implies dual unitarity
- Construction and the ergodicity properties of dual unitary quantum circuits
- Probing Operator Spreading via Floquet Engineering in a Superconducting Circuit
- 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
- Operator front broadening in chaotic and integrable quantum chains
- 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