Non-classical correlations versus quantum coherence in graphene lattice within the Hubbard model under intrinsic decoherence

Abstract

In this study, we explore the interplay between non-classical correlations and quantum coherence in graphene, modeled within the Hubbard framework, under the impact of the intrinsic decoherence effects. Employing concurrence (\({\mathcal {C}}\)) and uncertainty-induced nonlocality (\({\mathcal {U}}_{C}\)), we estimate the extent of entanglement and non-classical correlations, respectively, in the considered system, whereas quantum coherence is quantified through relative entropy of coherence (\({\mathcal {C}}_r\)). We assume that the graphene system is initially prepared in an extended Werner-like state and we examine the effect of purity of the initial state (p), Bloch angle (\(\theta\)), nearest-neighbor (V) and on-site (U) Coulomb interactions, and intrinsic decoherence (\(\gamma\)) on the dynamics of the three metrics of quantum correlations and coherence in the system. Our findings demonstrate that the \(\gamma\) rates negatively impact quantum resources in graphene. However, p and \(\theta\) play a pivotal role in generating and sustaining these resources, mitigating decoherence’s adverse effects over time. Additionally, our analysis underscores the crucial influence of U and V, which not only enhance quantum correlations and coherence but also stabilize the system against oscillatory behavior. By carefully optimizing U and V, it is possible to suppress the effects of intrinsic decoherence, ensuring robust quantum correlations and coherence within graphene.