A meaningful hierarchy of quantum resource quantifiers-comprising Bell nonlocality, Einstein-Podolsky-Rosen (EPR) steering, entanglement, and quantum discord (QD)-captures distinct nonclassical features essential for quantum information processing. In this study, we investigate the hierarchy of quantum resource quantifiers within condensed matter physics, using the two-dimensional Hubbard model as a framework for graphene systems with and without \(\mathcal{P}\mathcal{T}\) -symmetric operations. We focus on thermal Gibbs states at finite temperature as initial conditions, which exhibit varying degrees of entanglement depending on interaction parameters and temperature, with and without \(\mathcal{P}\mathcal{T}\) -symmetric operations. A detailed discussion is provided on how quantum resource quantifiers are affected by the thermal state equilibrium, the nearest- neighbor interaction \(V\) , and the on-site repulsion \(U\) . Our results numerically demonstrate how quantum resources in graphene are reduced or increased by modifying the strength of the short-range electron-electron Coulomb interaction. Additionally, findings confirm that the hierarchy of quantum resources is \(BN \le F S \le EI_{N }\le QD\) , where these measures coincide for pure bipartite states and separate for mixed states, especially under thermal noise and environmental interactions. Furthermore, we show that the invariance of this ranking in the thermal state and within the \(\mathcal{P}\mathcal{T}\) -symmetry framework leads directly to a specific sequence of sudden deaths. Moreover, we find that the simultaneous absence of sudden death for all forms of quantum nonlocality, except discord, occurs only for a measure-zero subset of states.
