Improved particle swarm optimization algorithm and its application to search for new magnetic ground states in the Hubbard model

An improved particle swarm optimization algorithm is proposed, and its superiority over the standard particle swarm optimization algorithm is tested on two typical benchmark functions. By employing this algorithm to search for the magnetic ground states of the Hubbard model on the real-space square lattice with finite size based on the mean-field approximation, two new magnetic states, namely, the double-striped-type antiferromagnetic state and the triple antiferromagnetic state, are found. We further perform mean-field calculations in the thermodynamical limit to confirm that these two new magnetic states are not a result of a finite-size effect, where the properties of the double-striped-type antiferromagnetic state are also presented.