Enhancing spin-spin correlations in the mixed-field Ising model with stochastic resetting

Recently was discovered that stochastic resetting in quantum systems may lead to the emergence of non-trivial correlations, even in the absence of intrinsic interactions. Here, we are interested in the mixed-field Ising (MFI) model subject to stochastic resetting, a protocol that interrupts the unitary evolution by returning the system to its initial state. We analyze analytically the two-point transverse correlations σ_i^xσ_j^x , in the limit without nearest neighbor interactions which reduces the system to an ensemble of Two-Level Systems (TLS), when being reset to the ferromagnetic state with maximal magnetization and find nontrivial resetting induced correlations. For a specific magnitude of the transverse field, the two-point transverse correlations reach a maximum, and increasing the field further only decorrelates the system. To obtain a deeper insight into the maximum of the correlations, we analyzed their dependence on both, the resetting rate and the external fields. Furthermore, using numerical techniques we study analytically inaccessible realizations of MFI, like the chaotic regime, and explore the effects of resetting on the internal unitary dynamics. Our results suggest that the two-point transverse correlations can be fine-tuned by the stochastic resetting and we concluded that some optimal range exists for the resetting rate parameter, which enhances those correlations.