Role of noise on defect formation and correlations in a long-range Ising model under adiabatic driving

Abstract We study an exactly solvable long-range (LR) transverse-field Ising model with a power-law decaying interaction characterized by the decay exponent α . For 1 < α < 2 , the model exhibits two quantum critical points with distinct critical exponents. In the thermodynamic limit, the system is adiabatically driven across these critical points in the presence of noise, from the paramagnetic phase with all spins down to one with all spins up. In the noiseless case, within the LR regime, the steady-state properties are primarily influenced by the modes near the k c = π region, while the low-energy modes around k c = 0 remain nearly adiabatic and contribute negligibly. The defect density follows Kibble–Zurek (KZ) scaling law and scales as n ∝ τ Q − 1 / 2 , implying KZ scaling exponent independent of decay exponent. However, the magnitude of the defect density increases with increasing the range (i.e. decreasing the value of α ). On the other hand in the presence of noise, the low-energy modes around k c = 0 become highly susceptible to excitation, making them the dominant source of excitations, with their contribution gradually diminishing as the interaction range increases. This differs from the short-range model, where previous studies have shown that under noisy condition modes around k = π / 2 play a significant role. The contrasting influence of LR interactions under noisy and noiseless driving, is also observed in spin–spin correlation function and defect distribution, highlighting how LR interactions fundamentally reshape the interplay between adiabatic driving and noise.