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.
