Frustrated electron liquids in the Hubbard model

TL;DR

This paper investigates the Hubbard model's ground state, revealing it as a frustrated Fermi liquid stabilized by Kondo and RVB mechanisms, and argues that a true Mott insulator cannot be the ground state at zero temperature.

Contribution

It introduces the supreme single-site approximation (S^3A) and demonstrates that the ground state is a frustrated Fermi liquid, challenging the notion of a Mott insulator as the ground state.

Findings

Ground state is a normal Fermi liquid in S^3A.

Fermi liquid is stabilized by Kondo effect and RVB mechanisms.

A Mott insulator cannot be the ground state at zero temperature.

Abstract

The ground state of the Hubbard model is studied within the constrained Hilbert space where no order parameter exists. The self-energy of electrons is decomposed into the single-site and multisite self-energies. The calculation of the single-site self-energy is mapped to a problem of self-consistently determining and solving the Anderson model. When an electron reservoir is explicitly considered, it is proved that the single-site self-energy is that of a normal Fermi liquid even if the multisite self-energy is anomalous. Thus, the ground state is a normal Fermi liquid in the supreme single-site approximation (S^3A). In the strong-coupling regime, the Fermi liquid is stabilized by the Kondo effect in the S^3A and is further stabilized by the Fock-type term of the superexchange interaction or the resonating-valence-bond (RVB) mechanism beyond the S^3A. The stabilized Fermi liquid is frustrated as much as an RVB spin liquid in the Heisenberg model. It is a relevant unperturbed state that can be used to study a normal or anomalous Fermi liquid and an ordered state in the whole Hilbert space by Kondo lattice theory. Even if higher-order multisite terms than the Fock-type term are considered, the ground state cannot be a Mott insulator. It can be merely a gapless semiconductor even if the multisite self-energy is so anomalous that it is divergent at the chemical potential. A Mott insulator is only possible as a high temperature phase.