Functional Integrals and Excitation Energy in Three-Band Hubbard Model

Jun Yan

The normal and anomalous Green's functions of antiferromagnetic state in three-band Hubbard model are studied by using functional integrals and temperature Green's function method. The equations of energy spectrum are derived. In addition, excitation energy of Fermi fields are calculated under long wave approximation.

Shiwei Zhang, Ettore Vitali, Adam Chiciak +1 more

W. D. Langer, Daniel Charles Mattis

Hiroyuki Kaga, Taiichirou Saikawa, Chihiro Ohmori

Magnetic susceptibilities of interacting (d) electrons in the Hubbard model and the three-band ${\mathrm{CuO}}_{2}$ model are worked out within the Gaussian fluctuations of the functional integral in the slave boson representation. The normalized Landau Fermi-liquid parameter |${\mathit{F}}_{0}^{\mathit{a}}$|/\ensuremath{\alpha} (\ensuremath{\alpha}\ensuremath{\equiv}${\mathit{W}}_{0}$${\mathit{N}}_{\mathit{F}}^{0}$, ${\mathit{N}}_{\mathit{F}}^{0}$ the density of states at the Fermi level, and ${\mathit{W}}_{0}$ the bare bandwidth) defined from the susceptibility expression is investigated for the two models as functions of Coulomb repulsion U, charge-transfer energy \ensuremath{\Delta}, and doping concentration \ensuremath{\delta}. It is shown that the Landau parameter for the three-band model is larger and exhibits different renormalization behaviors than that for the Hubbard model in both the weak- and strong-coupling regimes except in the Mott-Hubbard weak-coupling regime, where it takes the same random-phase approximation form U/${\mathit{W}}_{0}$ as the latter. The reasons for these results are analyzed. The slave-boson Landau parameter for the Hubbard model exactly reproduces the T-matrix expression |${\mathit{F}}_{0}^{\mathit{a}}$|/\ensuremath{\alpha}=U/${\mathit{W}}_{0}$/(1+U/${\mathit{W}}_{0}$) in the low-density limit, whose renormalization has the different origin from that in the dilutely doped regime. \textcopyright{} 1996 The American Physical Society.

Fa-jian Shi, Tsung-han Lin

With the aid of functional-integral technique, we show that the strongly correlated electron system described by the Hubbard model at finite temperature is approximately equivalent to the dynamically disordered electron system. For larger Coulomb interaction U, we show that it has localized states in the middle region of the band. Thus, the system exhibits a continuous metal-insulator transition, in which the activation energy for conduction is continuous, caused purely by the electron-electron interaction near half filling.

А. А. Овчинников