Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point

TL;DR

This paper investigates the quantum critical behavior of an infinite-range Ising ferromagnet under time-dependent transverse fields, revealing signatures of quantum phase transitions through quench and AC dynamics analysis.

Contribution

It develops a classical-quantum correspondence for the dynamics of the model and demonstrates how AC dynamics can reveal quantum critical points even in the classical limit.

Findings

AC dynamics show clear signatures of the quantum critical point.

Classical phase space analysis matches quantum dynamics near criticality.

Quantum critical behavior can be detected through classical dynamics signatures.

Abstract

We study an infinite range ferromagnetic Ising model in the presence of a transverse magnetic field which exhibits a quantum paramagnetic-ferromagnetic phase transition at a critical value of the transverse field. In the thermodynamic limit, the low-temperature properties of this model are dominated by the behavior of a single large classical spin governed by an anisotropic Hamiltonian. Using this property, we study the quench and AC dynamics of the model both numerically and analytically, and develop a correspondence between the classical phase space dynamics of a single spin and the quantum dynamics of the infinite-range ferromagnetic Ising model. In particular, we compare the behavior of the equal-time order parameter correlation function both near to and away from the quantum critical point in the presence of a quench or AC transverse field. We explicitly demonstrate that a clear signature of the quantum critical point can be obtained by studying the AC dynamics of the system even in the classical limit. We discuss possible realizations of our model in experimental systems.