Fermi-linearization scheme for itinerant electrons with Clifford variables

TL;DR

This paper introduces a novel Fermi-linearization scheme using Clifford variables for interacting electron systems, providing an analytical approach that captures key phenomena like metal-insulator transitions and reproduces known results in specific limits.

Contribution

It presents a new interpretation of Fermi-linearization with Clifford variables and applies it to the Falicov-Kimball model, deriving self-consistent solutions and connecting to phase transitions.

Findings

The scheme yields an order parameter-like coefficient.

It relates to metal-insulator transition behavior.

At zero temperature, reproduces Gutzwiller results for the Hubbard model.

Abstract

We propose here an alternative interpretation of the fermi-linarization approach to interacting electron systems, based on the requirement that the coefficients of the linearized operators are Clifford-like variables, whose anticommutator equals an unknown constant $c$. We apply the approximation to the Falicov-Kimball model, explicitly solving the self-consistency equation for the unknown, which turns out to behave as an order parameter. We discuss its relation with a metal-insulator transition and some thermodynamical quantities. In particular we show that our approximation in the $T=0$ limit reproduces exactly the Gutzwiller results for the Hubbard model.