Ferromagnetic-antiferromagnetic phase transition in the Hubbard model due to next-nearest electron hopping

The authors investigated the frustration effect when next-nearest-electron hopping causes itinerant ferromagnetism in a one-dimensional Hubbard model.By using the exact diagonalization method and the density-matrix renormalization-group technique,it was shown that the next-nearest electron hopping term stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n when the system is small.Furthermore,by calculating the local spin-spin correlation function,we found the ferromagnetic state becomes unstable as the length of the system increases.A further study showed that the ferromagnetic relationships of the system become weaker when the system's size increases.In addition,the system will transit to the anti-ferromagnetic correlation when the system reaches critical length.These observed results demonstrate on the one hand that an itinerant ferromagnetic phase exists in the electron-mixing area of small-sized material in the one-dimensional Hubbard model,and on the other hand,these observations should be helpful in understanding the origin of the itinerant ferromagnetism observed recently in some metallic and metallic oxide clusters.