Antiferromagnetism in the Hubbard model using 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. Following the U(1) formalism derived by Yu and Si [Phys. Rev. B 86, 085104 (2012)PRBMDO1098-012110.1103/PhysRevB.86.085104], it is shown 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. 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. While the Hubbard gap, the charge gap due to the doubly occupied states, scales with the Hubbard interaction U as expected, the AFM gap Δ, the gap in the spinon dispersion in the AFM state, exhibits a crossover from the weak- to strong-coupling behaviors as U increases. Our cluster slave-spin method reproduces not only the traditional mean-field behavior of Δ∼U in the weak-coupling limit, but also the behavior of Δ∼t2/U predicted by the superexchange mechanism in the strong-coupling limit. 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 quasiparticle weight obtained by the cluster slave-spin method is in a good agreement with the generalized Gutzwiller approximation in both AFM and paramagnetic states, and the results can be improved beyond the generalized Gutzwiller approximation 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.