Light cone in the two-dimensional transverse-field Ising model in time-dependent mean-field theory

TL;DR

This paper studies how local disturbances spread in a 2D transverse-field Ising model using time-dependent mean-field theory, revealing a transition from Manhattan to Euclidean light cone shapes and comparing velocities with exact 1D results.

Contribution

It introduces a mean-field approach based on the BBGKY hierarchy to analyze light cone propagation in 2D Ising models with time-dependent fields, highlighting metric transition effects.

Findings

Perturbations propagate with finite velocity forming light cones.

Transition from Manhattan to Euclidean metric in light cone shape.

Comparison of propagation velocities with 1D exact results.

Abstract

We investigate the propagation of a local perturbation in the two-dimensional transverse-field Ising model with a time-dependent application of mean-field theory based on the BBGKY hierarchy. We show that the perturbation propagates through the system with a finite velocity and that there is transition from Manhattan to Euclidian metric, resulting in a light cone with an almost circular shape at sufficiently large distances. The propagation velocity of the perturbation defining the front of the light cone is discussed with respect to the parameters of the Hamiltonian and compared to exact results for the transverse-field Ising model in one dimension.