One Dimensional Kondo Lattice Model Studied by the Density Matrix Renormalization Group Method

TL;DR

This review discusses recent theoretical advances in the one-dimensional Kondo lattice model using the DMRG method, highlighting metallic and insulating phases, excitation gaps, and temperature-dependent properties.

Contribution

It provides a comprehensive overview of DMRG applications to the 1D Kondo lattice model, including finite-temperature and dynamic properties, with new insights into Fermi surface behavior and excitation spectra.

Findings

Paramagnetic metallic state is a Tomonaga-Luttinger liquid with a large Fermi surface.

At half-filling, the ground state is insulating with various excitation gaps.

Temperature dependence reveals unusual properties of Kondo insulators.

Abstract

Recent developments of the theoretical investigations on the one-dimensional Kondo lattice model by using the density matrix renormalization group (DMRG) method are discussed in this review. Short summaries are given for the zero-temperature DMRG, the finite-temperature DMRG, and also its application to dynamic quantities. Away from half-filling, the paramagnetic metallic state is shown to be a Tomonaga-Luttinger liquid with the large Fermi surface. For the large Fermi surface its size is determined by the sum of the densities of the conduction electrons and the localized spins. The correlation exponent K_rho of this metallic phase is smaller than 1/2. At half-filling the ground state is insulating. Excitation gaps are different depending on channels, the spin gap, the charge gap and the quasiparticle gap. Temperature dependence of the spin and charge susceptibilities and specific heat are discussed. Particularly interesting is the temperature dependence of various excitation spectra, which show unusual properties of the Kondo insulators.