The Marginal Fermi Liquid - An Exact Derivation Based on Dirac's First Class Constraints Method

TL;DR

This paper derives the Marginal Fermi Liquid behavior using Dirac's first class constraints method, showing how constraints influence electron correlations and spectral properties in correlated electron systems.

Contribution

It introduces an exact derivation of the Marginal Fermi Liquid from Dirac's constraints, linking electron exclusion principles to spectral asymmetries and self-energy characteristics.

Findings

Imaginary part of self-energy is linear in frequency.

At high hole concentrations, Fermi Liquid behavior emerges.

Constraints cause electron-hole spectral asymmetry.

Abstract

Dirac's method for constraints is used for solving the problem of exclusion of double occupancy for Correlated Electrons. The constraints are enforced by the pair operator $Q(\vec{x})=\psi_{\downarrow}(\vec{x})\psi_{\uparrow}(\vec{x})$ which annihilates the ground state $|\Psi^0>$. Away from half fillings the operator $Q(\vec{x})$ is replaced by a set of $first$ $class$ Non-Abelian constraints $Q^{(-)}_{\alpha}(\vec{x})$ restricted to negative energies. The propagator for a single hole away from half fillings is determined by modified measure which is a function of the time duration of the hole propagator. As a result: a) The imaginary part of the self energy - is linear in the frequency. At large hole concentrations a Fermi Liquid self energy is obtained. b) For the Superconducting state the constraints generate an asymmetric spectrum excitations between electrons and holes giving rise to an asymmetry tunneling density of states.