Broken symmetry solutions of the two dimensional extended Hubbard model and their instability conditions

Masa-aki Ozaki, Shoji Yamamoto

Shoji Yamamoto, Masa-aki Ozaki

Abstract Instabilities of the restricted Hartree–Fock (HF) state of the two‐dimensional extended Hubbard model under doping are studied with the linear response theory employing the linearized Bethe–Salpeter equation. Boundaries of the instabilities for the ordering vectors q = Q ≡ (π, π) and q = Q0 ≡ (0, 0) are given in terms of the interaction strength parameters at various doping levels. With doping, dominant instabilities generally change from ones for q = Q to ones for q = Q0. Broken symmetry phases obtained from the instabilities are also studied and classified using the group‐theoretical technique. For q = Q, two more new phases are obtained in addition to the four nonmagnetic and five magnetic phases that have been already derived by one of the authors. For q = Q0, three nonmagnetic and five magnetic phases are obtained. Deriving the explicit forms of the charge current and spin current operators in the HF approximation, charge current and spin current densities in the broken symmetry states are discussed in detail. © 1992 John Wiley & Sons, Inc.

S. A. Trugman

Carsten Honerkamp A

We review recent developments in functional renormalization group (RG) methods for interacting fermions. These approaches aim at obtaining an unbiased picture of competing Fermi liquid instabilities in the low-dimensional models like the two-dimensional Hubbard model. We discuss how these instabilities can be approached from various sides and how the fermionic RG flow can be continued into phases with broken symmetry.

M. S. Laad, Dipan K. Ghosh

Arne Neumayr, Walter Metzner

Divergencies appearing in perturbation expansions of interacting many-body systems can often be removed by expanding around a suitably chosen renormalized (instead of the noninteracting) Hamiltonian. We describe such a renormalized perturbation expansion for interacting Fermi systems, which treats Fermi surface shifts and superconductivity with an arbitrary gap function via additive counterterms. The expansion is formulated explicitly for the Hubbard model to second order in the interaction. Numerical solutions of the self-consistency condition determining the Fermi surface and the gap function are calculated for the two-dimensional case. For the repulsive Hubbard model close to half-filling we find a superconducting state with d-wave symmetry, as expected. For Fermi levels close to the van Hove singularity a Pomeranchuk instability leads to Fermi surfaces with a broken square lattice symmetry, whose topology can be closed or open. For the attractive Hubbard model the second-order calculation yields an s-wave superconductivity with a weakly momentum dependent gap, whose size is reduced compared to the mean-field result.