Solution of one-dimensional Kondo lattice model, ground state calculation

TL;DR

This paper analyzes the ground state of the one-dimensional Kondo lattice model, revealing the formation of local singlet states, their scattering properties, and the resulting charge gap behavior across interaction strengths.

Contribution

It provides a detailed calculation of the ground state considering local singlet formation and the charge gap for arbitrary exchange interactions using Bethe Ansatz.

Findings

Electrons do not hybridize with local moments.

A lattice with a double cell is not formed.

Charge gap depends on interaction strength, proportional to the square of the exchange integral in weak coupling.

Abstract

The ground state of the Kondo chain is calculated taking into account the formation of local singlet states of electrons and moments. Singlets are entangled local states of electrons and moments arranged chaotically and varying in time. Two-particle scattering matrix of electrons forming singlets is calculated using the Bethe Ansatz. It is shown that electrons do not hybridize with local moments, and a lattice with a double cell is not formed. In the Kondo insulator a charge gap is calculated for an arbitrary value of the exchange integral. In the case of strong interaction the gap is determined by the single-particle energy of the singlet, for weak interaction - by correlations (the gap is proportional to the square of the exchange integral).