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 a 0 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 a 0 = −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 s 0 is lowered near half filling by increasing U when the intersite Coulomb interaction V is attractive, but in contrast to F a 0 at J < 0 it requires an attraction beyond a critical value V c to generate the divergence of the charge susceptibility at F s 0 = −1 in the metallic phase. This instability was found for a broad range of electronic filling away from half filling for moderate attraction.

Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory

“…A further question is raised due to the nonsymmetrized notation used in this work for the vertex function F kk q and the fermion-boson response L kq . For example, in the latter case the relation (14) to the threeleg vertex Λ kq seems problematic, L kq = G k G k+q Λ kq , due to the ambiguous static homogeneous limit of the non-symmetrized bubble G k G k+q . To resolve the issue, we define the symmetrized static homogeneous limit of L and F as follows,…”

“…On the other hand, when a Landau parameter f approaches the value −1, in general [13] a Pomeranchuk instability occurs, which can be favored by non-local interactions [14]. The symmetric Landau parameter of a multi-orbital Hubbard model in the so-called Hund's metal regime has recently been calculated using the slavespin method [15,16], which predicts a phase separation as an instability of the Mott insulator upon doping [17] which takes place just above the critical interaction strength for the Mott transition.…”

Magnetic Spin Susceptibility of quasi-particles in metals using the Landau Fermi Liquid Theory

“…These Landau parameters describe how the elementary excitations of the Fermi Liquid that is the quasi-particles and quasiholes interact with one another [4,5]. The instabilities in spin and charge channels for Landau parameters in the non-degenerate extended using Hubbard model with intersite coloumb and exchange interaction was investigated by Lhoutellier et al, [6]. The inverse propagator was determined using spin rotational invariant slave boson approach.…”

The extended Hubbard model with attractive interactions

“…Strong nearest-neighbor repulsion leads to a charge-ordered state. The phase transition line from the Fermi liquid to this ordered phase has been determined in several computational approaches [15,16,17,18,19,20,21,22,23,24,25,26,27] and currently serves as the main way to compare these methods. In the attractive V < 0 regime, a second transition occurs, now to a phase separation into a high and a low density state [23,28].…”

“…The phase transition line from the Fermi liquid to this ordered phase has been determined in several computational approaches [15,16,17,18,19,20,21,22,23,24,25,26,27] and currently serves as the main way to compare these methods. In the attractive V < 0 regime, a second transition occurs, now to a phase separation into a high and a low density state [23,28]. Our purpose is to use this transition as a new benchmark for computational approaches to the extended Hubbard model.…”