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It turns out that the ground states of some systems are symmetry-brokenstates in which some property is not symmetrically distributed. In the case ofstrongly correlated electron systems, that were studied by the DFT+U method,researchers had shown that the total energy of the system is a multi-minimafunction of input parameters and one has to single out the ground state out ofthe couples of minimum-energy states. However, the methods already introducedto determine these local minimum states were not able to predict all suchstates which may include the "true" ground state. In this work, we introduce anew simple and straight-forward method of SMC to find the GS as well as themeta-stable states of 1k-order anti-ferromagnetic configuration for UO$_2$.Using this method, it is shown that the ground state of UO$_2$ system is aspin-symmetry broken state of the electron spin magnetizations of oxygen atoms.Depending on the way we apply the SMC method, we obtain different numbers ofmeta-stable states, but the same ground states. The energetic properties,geometric properties, the electronic density distributions, and the electronicpolarization density distributions of the ground state and the meta-stablestates are shown to be different from each other. These properties also areshown to be sensitive to the magnitude of the initial opposite magnetizationsof U1 and U2 atoms in the 1k-order anti-ferromagnetic configuration, but thenumber of meta-stable states as well as the ground-state properties areinsensitive to this magnitude. Using the PBEsol-GGA approximation for theexchange-correlation we obtain the ground-state properties in excellentagreement with experiments.

Spin-Symmetry Broken Ground-State of UO$_2$ in DFT+U Approach: The SMC Method