Phase transitions in the Hubbard model studied by a cluster slave spin method

The cluster slave-spin method is introduced to systematically investigate the solutions of the Hubbard model including the symmetry-broken phases. In this method, the electron operator is factorized into a fermionic spinon describing the physical spin and a slave-spin describing the charge fluctuations. We show that the self-consistent equations to explore various symmetry-broken density wave states can be constructed in general with a cluster of multiple slave-spin sites, and we employ this method to study the antiferromagnetic (AFM) state in the single band Hubbard model with the two- and four-site clusters of slave spins. We find that the cluster slave-spin method can capture correct behaviors in both weak- and strong- coupling limit within a unified framework. In addition, the holon-doublon correlator as functions of U and doping x is also computed, which exhibits a strong tendency toward the holon-doublon binding in the strong coupling regime. We further show that the results are progressively improved as the cluster is enlarged from a single site to four sites. Our results demonstrate that the cluster slave-spin method can be a powerful tool to systematically investigate the strongly correlated system.