The failure of semiclassical approach in the dissipative fully-connected Ising model

TL;DR

This paper investigates the dissipative fully-connected Ising model under periodic driving, revealing that the semiclassical approach fails to accurately predict the system's behavior at large field amplitudes, where the exact solution remains periodic.

Contribution

The study demonstrates the failure of the semiclassical approximation in the dissipative fully-connected Ising model at large field amplitudes, supported by numerical and spectral analysis.

Findings

Semiclassical approach predicts chaos at large field amplitudes.

Exact numerical simulations show persistent periodic response.

Spectral analysis confirms periodicity in the thermodynamic limit.

Abstract

We solve the fully-connected Ising model in the presence of dissipation and time-periodic field, with the corresponding Lindblad equation having a time-periodic Liouvillian. The dynamics of the magnetizations is studied by using both the semiclassical approach and the numerical simulation with the help of permutation symmetry. The semiclassical approach shows a transition from the periodic response for small field amplitude to the chaotic dynamics for large amplitude. The trajectory of the magnetizations and the Lyapunov exponents are calculated, which support the existence of a chaotic phase. But in the exact numerical simulation, the response is periodic for both small and large amplitude. The scaling analysis of Floquet Liouvillian spectrum confirms the periodic response in the thermodynamic limit. The semiclassical approximation is found to fail as the field amplitude is large.