Information spreading and scrambling in disorder-free multiple-spin interacting models

TL;DR

This paper investigates how disorder-free multi-spin interactions influence information scrambling, revealing non-linear light-cone dynamics, early logarithmic growth, and phase-transition-like behavior of tripartite mutual information, contrasting with conventional models.

Contribution

It provides numerical analysis of TMI in disorder-free spin models with multi-spin interactions, highlighting their nearly integrable nature and impact on information spreading.

Findings

TMI does not show linear light-cone in these models.

Early-time TMI increases logarithmically, unlike linear growth in conventional models.

Late-time TMI indicates a phase transition related to integrability.

Abstract

Tripartite mutual information (TMI) is an efficient observable to quantify the ability of scrambler for unitary time-evolution operator with quenched many-body Hamiltonian. In this paper, we give numerical demonstrations of the TMI in disorder-free (translational invariant) spin models with 3-body and 4-body multiple-spin interactions. The dynamical behavior of the TMI of these models does {\it not} exhibit linear light-cone for sufficiently strong interactions. In early-time evolution, the TMI displays distinct negative increase behavior fitted by a logarithmic-like function. This is in contrast to the conventional linear light-cone behavior present in the XXZ model and its near integrable vicinity. The late-time evolution of the TMI in finite-size systems is also numerically investigated. The multiple-spin interactions make the system nearly integrable and weakly suppress the spread of information and scrambling. The observation of the late-time value of the TMI indicates that the scrambling nature of the system changes by interactions and this change can be characterized by a phase-transition-like behavior of the TMI, reflecting the system's integrability and breaking of eigenstate thermalization hypothesis.