Generalized susceptibilities and Landau parameters for anisotropic Fermi liquids

TL;DR

This paper develops a framework for calculating susceptibilities and Landau parameters in anisotropic Fermi liquids with arbitrary interactions, extending traditional isotropic models to more general Fermi surface geometries.

Contribution

It introduces generalized formulas for static susceptibilities and proposes a new definition of Landau parameters for anisotropic Fermi liquids.

Findings

Derived explicit expressions for generalized susceptibilities.

Applied formulas to spin and charge responses.

Proposed a novel definition of Landau parameters for anisotropic systems.

Abstract

We study Fermi liquids with a Fermi surface that lacks continuous rotational invariance, and in the presence of an arbitrary quartic interaction. We obtain the expressions of the generalized static susceptibilities that measure the linear response of a generic order parameter to a perturbation of the Hamiltonian. We apply our formulae to the spin and charge susceptibilities. Based on the resulting expressions, we make a proposal for the definition of the Landau parameters in non-isotropic Fermi liquid.