Fermi liquid in the Hubbard Model with an electron reservoir: Normal state of cuprate superconductors

TL;DR

This paper proves that the normal state of the Hubbard model with an electron reservoir is a Fermi liquid under certain approximations, stabilized by the Kondo effect and RVB mechanisms, relevant to cuprate superconductors.

Contribution

It demonstrates that the Fermi liquid state persists in the Hubbard model with an electron reservoir under common approximations, highlighting stabilization mechanisms.

Findings

Fermi liquid state exists under S^3A, DMFT, DCPA approximations

Kondo effect stabilizes local singlets in strong coupling

RVB mechanism further stabilizes the Fermi liquid

Abstract

It is proved that the ground state under the supreme single-site approximation (S^3A), the dynamical mean-field theory (DMFT), or the dynamical coherent potential approximation (DCPA) is the normal Fermi liquid in the presence of an infinitesimally weak hybridization with an electron reservoir, except for the just half filling of electrons and the infinite on-site repulsion. In the strong-coupling regime, in particular, the Fermi liquid is stabilized under S^3A, DMFT, or DCPA by the Kondo effect, which stabilizes a local singlet on each unit cell, and is further stabilized beyond it by the Fock-type term of the superexchange interaction or a resonating valence bond (RVB) mechanism, which stabilizes a local singlet on each pair of nearest neighbors. The Fermi liquid is a relevant normal state to study possible lower-temperature phases or the true ground state. It is proposed that the Fermi liquid stabilized by the Kondo effect and the RVB mechanism is the normal state of cuprate high-temperature superconductors.