Mechanisms of scrambling and unscrambling of quantum information in the ground state in spin chains: domain-walls, spin-flips and scattering phase shifts

Abstract

The spatiotemporal evolution of the out-of-time-order correlator (OTOC) measures the propagation and scrambling of local quantum information. For the transverse field Ising model with open boundaries, the local operator ${\sigma }^x$ shows an interesting picture of the ground state OTOC where the local information gets scrambled throughout the entire system and, more strikingly, starts `unscrambling' upon reflection at the other end. Earlier discussions of OTOCs did not explain the physical processes responsible for such scrambling and unscrambling of information. We explicitly show that in the paramagnetic phase, the scrambling and unscrambling is due to the scattering of a pair of low-energy spin-flip excitations, even in the presence of small interactions. In the ferromagnetic phase the same phenomena are explained by the motion of a domain-wall excitation. Thus, in different limits of the system parameters, we have provided a simple and almost complete understanding of the space-time pictures of the OTOCs, including the unscrambling, in terms of the low-energy excitations like one and two spin-flips or a single domain wall.

arXiv comment6+4 pages, 6 figures

References in corpus (35)

• A bound on chaos
• Black holes and the butterfly effect
• Operator Spreading in Random Unitary Circuits
• Chaos in quantum channels
• 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
• Lieb-Robinson and the butterfly effect
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Slow scrambling in disordered quantum systems
• Scrambling and thermalization in a diffusive quantum many-body system
• Does scrambling equal chaos?
• Scrambling and entanglement spreading in long-range spin chains
• Out-of-time-ordered correlators in quantum Ising chain
• Information propagation in isolated quantum systems
• Detecting equilibrium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators
• Quantum butterfly effect in weakly interacting diffusive metals
• Out-of-Time-Order Correlation at a Quantum Phase Transition
• Thermodynamics of quantum information scrambling
• Out-of-time-ordered density correlators in Luttinger liquids
• Scrambling of Quantum Information in Quantum Many-Body Systems
• Scrambling is Necessary but Not Sufficient for Chaos
• Detection of quantum phases via out-of-time-order correlators
• Out of Time Ordered Correlators and Entanglement Growth in the Random Field XX Spin Chain
• Slow growth of out-of-time-order correlators and entanglement in integrable disordered systems
• Out-of-time-order correlations and Floquet dynamical quantum phase transition
• Scrambling in the Dicke model
• Hierarchy of Information Scrambling, Thermalization, and Hydrodynamic Flow in Graphene
• Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
• Operator front broadening in chaotic and integrable quantum chains
• Quantum caustics and the hierarchy of light cones in quenched spin chains
• Hydrodynamic theory of scrambling in chaotic long-range interacting systems
• Out-of-Time-Order Correlators in One-Dimensional XY model
• Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain
• Information scrambling and redistribution of quantum correlations through dynamical evolution in spin chains