Spatial deformation of many-body quantum chaotic systems and quantum information scrambling

TL;DR

This paper investigates how spatial inhomogeneity affects quantum information scrambling in many-body systems, demonstrating control over scrambling dynamics via Hamiltonian modulation and revealing black-hole-like energy behaviors.

Contribution

It introduces the study of spatially modulated Hamiltonians in quantum chaotic systems, showing how inhomogeneity can control information scrambling and exhibit black-hole-like energy signatures.

Findings

Spatial inhomogeneity can suppress or accelerate quantum information scrambling.

Modulating Hamiltonian density allows control over the butterfly effect.

Energy density dynamics show black-hole-like signatures in chaotic spin chains.

Abstract

We study the effect of spatial inhomogeneity on quantum information scrambling, a process of spreading and locally hiding quantum information in quantum many-body systems. As a paradigmatic example, we consider the quantum chaotic Ising spin chain and its inhomogeneous counterpart that is obtained by modulating the Hamiltonian density. Specifically, we consider the so-called M\"obius and sine-square deformations that were previously studied in the context of (1+1)-dimensional conformal field theories ($1+1$ d CFTs). In the spatial region where the modulated energy density is small, these deformations prevent the spreading of quantum information while in the region where the modulated energy density is large quantum information scrambling is accelerated. This suggests that we can control the scrambling and butterfly effect by spatially modulating the Hamiltonian density. We also found that the time dependence of energy density exhibits the signature of black-hole-like excitation found in the $1+1$ d CFTs even in the chaotic spin chain.