  The kernel of the study of magnetic quantum materials focuses on the magnetic
phase transitions, among which the most common phenomenon is the transition
between low-temperature magnetic-ordered phase to high-temperature paramagnetic
phase. A paramount question is if such paramagnetic phase of the correlated
solids can be well described by single-particle band theory to facilitate the
experimental observations. In this work, we investigate the properties of
temperature-driven paramagnetic phase via two different approaches within the
framework of density functional theory, monomorphous and polymorphous
description. From a comprehensive comparison of total energies, symmetries and
band structures, we demonstrate the necessity for a proper treatment of
paramagnetic phases with several prototypical examples. For Pauli paramagnetism
phase, the vanishing of spin moments permits us to apply a nonmagnetic
monomorphous description, while for paramagnetism with disordered local
moments, such description imposes unrealistic high symmetry, leading to a
metallic state in certain cases, inconsistent with the experimental
observation. In contrast, the polymorphous description based on a large-enough
supercell with disordered local moments is able to count in the effects of
distinct local environments, such as symmetry lowing, providing a more reliable
paramagnetic electronic structure and total energy compared with experiments.
Our work shed new insights on discovering the temperature-dependent magnetic
phase transition in the field of magnetic quantum materials.
