Fermi-liquid Landau parameters for a nondegenerate band: Spin and charge instabilities in the extended Hubbard model

Abstract

We investigate the Landau parameters for the instabilities in spin and charge channels in the nondegenerate extended Hubbard model with intersite Coulomb and exchange interactions. To this aim we use the spin rotationally invariant slave boson approach and we determine the necessary inverse propagator matrix. The analytically derived spin Landau parameter $F_0^a$ for the half filled band uncovers the intrinsic instability of the nondegenerate Hubbard model towards ferromagnetism --- negative intersite exchange interaction triggers a ferromagnetic instability at half filling before the metal-insulator transition, indicated by the divergence of the magnetic susceptibility at $F_0^a=-1$. This result is general and the instability occurs in the strongly correlated metallic regime for any lattice, in three or two dimensions. Next as an illustrative example we present numerical results obtained for the cubic lattice with nearest neighbor exchange $J$ and Coulomb $V$ elements and arbitrary electron density. One finds that the range of small doping near half filling is the most unstable one towards spin polarization, but only in the case of ferromagnetic intersite exchange $J<0$. Charge Landau parameter $F_0^s$ is lowered near half filling by increasing $U$ when the intersite Coulomb interaction $V$ is attractive, but in contrast to $F_0^a$ at $J<0$ it requires an attraction beyond a critical value $V_c$ to generate the divergence of the charge susceptibility at $F_0^s=-1$ in the metallic phase. This instability was found for a broad range of electronic filling away from half filling for moderate attraction.

arXiv comment12 pages, 10 figures

References in corpus (33)

• Functional renormalization group approach to correlated fermion systems
• From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model
• Ferromagnetism in the Hubbard Model-- Examples from Models with Degenerate Single-Electron Ground States
• Renormalization group analysis of the 2D Hubbard model
• Multi-band Gutzwiller wave functions for general on-site interactions
• Landau Theory of the Finite Temperature Mott Transition
• Ferromagnetism in the two dimensional t-t' Hubbard model at the Van Hove density
• Magnetic and superconducting instabilities of the Hubbard model at the van Hove filling
• Long-range Coulomb interactions in surface systems: a first principles description within self-consistently combined GW and dynamical mean field theory
• Unidirectional d-wave superconducting domains in the two-dimensional t-J model
• Magnetic fluctuations from stripes in cuprates
• Ferromagnetism, paramagnetism and a Curie-Weiss metal in an electron doped Hubbard model on a triangular lattice
• Metallic mean-field stripes, incommensurability and chemical potential in cuprates
• Proposed realization of itinerant ferromagnetism in optical lattices
• Magnetic phases near the Van Hove singularity in s- and d-band Hubbard model
• Non-perturbative approaches to magnetism in strongly correlated electron systems
• Ferromagnetic Properties of ZrZn${}_2$
• Unrestricted slave-boson mean-field approximation for the two-dimensional Hubbard model
• Dynamics of metallic stripes in cuprates
• Interplay between incommensurate phases in the cuprates
• Exact Results on Itinerant Ferromagnetism in Multi-orbital Systems on Square and Cubic Lattices
• Slave-boson approach to the metallic stripe phases with large unit cells
• Spin and Charge Structure Factor of the 2-d Hubbard Model
• What about U on Surfaces? - Extended Hubbard Models for Adatom Systems from First Principles
• Slave bosons in radial gauge: a bridge between path integral and hamiltonian language
• Slave Bosons in Radial Gauge: the Correct Functional Integral Representation and Inclusion of Non-Local Interactions
• Effects of inter-site Coulomb interactions on ferromagnetism: Application to Fe, Co and Ni
• Charge and spin transport through a ferromagnet/insulator/unconventional superconductor junction
• Magnetic and Charge Correlations of the 2-dimensional $t-t^{\prime }-U$ Hubbard model
• Interface controlled electronic charge inhomogeneities in correlated heterostructures
• Exact results with the Kotliar-Ruckenstein slave-boson representation
• Dispersion-driven ferromagnetism in a flat-band Hubbard system
• Exotic spin, charge and pairing correlations of the two-dimensional doped Hubbard model: a symmetry entangled mean-field approach

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