arXiv:cond-mat/9512160

Spin-reflection positivity of the Kondo lattice at half-filling

Takashi Yanagisawa, Yukihiro Shimoi

Published Dec 22, 1995• 0 citations

Abstract

We examine the spin-reflection positivity of the ground state of the Kondo lattice model at half-filling with the antiferromagnetic and ferromagnetic exchange couplings $J\ne0$. For every positive $U>0$, where U is the Coulomb interaction between the conduction electrons, we can show that the ground state is unique.

DOI: 10.48550/arxiv.cond-mat/9512160

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arXiv:cond-mat/9512160

Spin-reflection positivity of the Kondo lattice at half-filling

Takashi Yanagisawa, Yukihiro Shimoi

Published Dec 22, 1995• 0 citations

arXiv HTML PDF

Abstract

We examine the spin-reflection positivity of the ground state of the Kondo lattice model at half-filling with the antiferromagnetic and ferromagnetic exchange couplings

J\ne0

. For every positive

U>0

, where U is the Coulomb interaction between the conduction electrons, we can show that the ground state is unique.

DOI: 10.48550/arxiv.cond-mat/9512160

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arXiv:2202.03708Physical review. B./Physical review. BJul 14, 20225 citations

We examine the spin-reflection positivity of the ground state of the Kondo lattice model at half-filling with the antiferromagnetic and ferromagnetic exchange couplings

J\ne0

. For every positive

U>0

, where U is the Coulomb interaction between the conduction electrons, we can show that the ground state is unique.

We investigate the ground state of the Kondo-Hubbard model employing the recently introduced idea of spin-reflection positivity. It is shown exactly that the Kondo-Hubbard model for

J<0

and

U>|J|/4

at half filling has a unique ground state which can be ferromagnetic or singlet according to the lattice structure. In particular, for the Kondo lattice with

U>|J|/4

, the ground state is a singlet. We also show a theorem for the Kondo-Hubbard model with the anisotropic antiferromagnetic coupling ${J}_{\ensuremath{\perp}}>0$ and ${J}_{z}\ensuremath{\le}0$ for

U>|{J}_{z}|/4

We study higher-spin ($S\ensuremath{\ge}1$) generalization of the one-dimensional Kondo-Heisenberg model, in which the local spin-

S

moments of the Kondo-lattice model interact with each other via the antiferromagnetic Heisenberg interaction (

{J}_{\text{H}}

), by analytical and numerical methods. The strong-coupling (i.e., large Kondo coupling) expansion maps out an insulating phase at half-filling whose magnetic correlation depends on the parity of

2S

as well as a ferromagnetic metallic phase which dominates the strong-coupling region at generic fillings. Then, we carried out the density-matrix renormalization-group simulations for

S=1

to closely investigate the phase structure at large but finite Kondo coupling. At half-filling, the Kondo coupling and

{J}_{\text{H}}

do not compete and the insulating spin-gapless phase is stable, while the competition of the two leads to a stepwise collapse of the strong-coupling ferromagnetism via an intervening dimerized insulating phase with power-law spin correlation at quarter-filling.