Auxiliary boson approach for electronic states in the two-dimensional Hubbard model

Abstract

Electronic states in the two-dimensional Hubbard model are studied in the doped paramagnetic states by use of the auxiliary boson approach. Four auxiliary bosons are introduced by means of the Hubbard-Stratonovich transformation within the functional integral treatment. These bosons correspond to one charge and three spin fluctuations. An effective model is formulated. Going beyond the boson fluctuations around the saddle point, the single-electron Green's function including one-loop self-energy effects of fermion-boson interaction is derived. The behavior of the fermion self-energy, spectral functions, and density of states are investigated for several values of the Coulomb interaction $U$ within the limit imposed by the Stoner criterion and also for small and moderate doping concentrations $\ensuremath{\delta}$. For small doping $(\ensuremath{\delta}=0.2)$, as $U$ approaches a value determined by the Stoner criterion, the spin-boson spectrum has a striking low-energy enhancement around $\mathbf{q}\ensuremath{\sim}2{\mathbf{k}}_{F}.$ This enhancement of the spin fluctuation causes a non-Fermi-liquid-like low-energy $\ensuremath{\omega}$ linear dependence in the imaginary part of the self-energy. Due to the self-energy effects, band splittings and a band narrowing are produced in the spectral functions. As a consequence of this, the density of states has pseudogap structures around the quasiparticle band with a narrow bandwidth on the Fermi energy. These features seem to be precursors of the metal-insulator (Mott-Hubbard) transition and they might be related to the spin-gap phenomena observed in high-${T}_{c}$ materials. Our results for the density of states, the spectral function, and the band dispersions show qualitative agreement with the data of finite-size cluster simulations.