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

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.

6 pages, 4 figures

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Cited by in corpus (3)

• Quantum dynamics in transverse-field Ising models from classical networks
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Quench dynamics of quantum spin models with flat bands of excitations