Asian Journal of Advanced Research and Reports

Condensed matter physics increasingly depends on computation to explain how collective behaviour emerges from interacting electrons, spins and lattices, and to anticipate which materials will host unconventional superconductivity, quantum spin liquids, topological phases or correlated states in two-dimensional moiré superlattices. Methodological progress has been rapid, yet the literature remains divided into method-specific reviews that seldom ask a common question: how far can a computational conclusion about an emergent phenomenon be trusted, and what evidence establishes that trust? This critical narrative review addresses that question for theoretical and computational studies of quantum materials published between January 2004 and September 2026, supplemented by foundational earlier work. Literature was identified through multidisciplinary and physics-relevant scholarly indexes, citation tracing and examination of benchmark studies, and was appraised for control of approximations, convergence and finite-size analysis, agreement across independent methods, reproducibility and the quality of experimental confrontation. The synthesis indicates that density functional theory and its high-throughput extensions are dependable for structural energetics, phonon-mediated superconductivity and symmetry-indicated band topology when the relevant correlations are weak, whereas their conclusions for magnetic and correlated materials depend strongly on the exchange–correlation approximation. Embedding theories, tensor networks and quantum Monte Carlo methods have converged on several model ground states, most clearly the stripe-dominated physics of the two-dimensional Hubbard model. By contrast, the kagome antiferromagnet, Kitaev materials, nickelate superconductors and fractional Chern insulators illustrate persistent disagreement driven by model construction, parameter sensitivity and finite-size effects. Machine-learned potentials and wavefunctions extend accessible length and time scales but introduce dataset-dependent biases, and claims of quantum computational advantage for materials problems have repeatedly been narrowed by improved classical algorithms. The review proposes a tiered framework that treats internal verification, cross-method convergence and prospective experimental falsification as successive levels of predictive reliability. Priorities include uncertainty-quantified construction of low-energy models, shared benchmarks for realistic multi-orbital Hamiltonians and prospective tests of computational predictions. Computational condensed matter physics has become genuinely predictive in specific, well-characterised regimes; the principal task now is to state explicitly where those regimes end.