Physical review. B, Condensed matter

Spin-liquid ground state of the half-filled Kondo lattice in one dimension

Hirokazu Tsunetsugu, Yasuhiro Hatsugai, Kazuo Ueda, Manfred Sigrist

Published Aug 1, 1992• 136 citations

Abstract

By finite-size analysis of exact diagonalization the existence of a finite spin gap is confirmed for both antiferromagnetic and ferromagnetic coupling in the half-filled Kondo lattice model. For all finite values of antiferromagnetic coupling the system belongs to a class of coherent Kondo spin singlet, whereas for any finite ferromagnetic coupling it scales to a spin S=1 antiferromagnetic chain with a Haldane gap.

DOI: 10.1103/physrevb.46.3175

Related papers

Ground State of the Kondo-Hubbard Model at Half Filling

Takashi Yanagisawa, Yukihiro Shimoi

Physical Review LettersJun 12, 199532 citations

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

Takashi Yanagisawa, Yukihiro Shimoi

arXiv:cond-mat/9512160Dec 22, 19950 citations

Singlet ground state of the periodic Anderson model at half filling: A rigorous result

Kazuo Ueda, Hirokazu Tsunetsugu, Manfred Sigrist

It is proved that the ground state of the symmetric periodic Anderson model forms a total spin singlet at half filling. This result can also be applied to the Kondo lattice model, at least for the weak and the very strong antiferromagnetic-coupling limit. For the strong coupling limit of the Kondo lattice it is additionally proved that the singlet ground state exists even when two holes are doped to the half-filled band.

Physical Review LettersFeb 17, 199293 citations

Spin correlations in dense Kondo systems

Paolo Maria Santini, Jenő Sólyom, Lucio Claudio Andreani +1 more

Journal of Applied PhysicsMay 15, 19931 citation

Electric and magnetic properties of higher-spin Kondo-Heisenberg models at strong coupling

Riku Masui, Keisuke Totsuka

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

Quantum Monte Carlo Simulations of the Half-Filled Two-Dimensional Kondo Lattice Model

Fakher F. Assaad

arXiv:cond-mat/9904178Physical Review LettersJul 26, 1999134 citations

Physical review. B, Condensed matter

Spin-liquid ground state of the half-filled Kondo lattice in one dimension

Hirokazu Tsunetsugu, Yasuhiro Hatsugai, Kazuo Ueda, Manfred Sigrist

Published Aug 1, 1992• 136 citations

Publisher

Abstract

DOI: 10.1103/physrevb.46.3175

Related papers

Ground State of the Kondo-Hubbard Model at Half Filling

Takashi Yanagisawa, Yukihiro Shimoi

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

Physical Review LettersJun 12, 199532 citations

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

Takashi Yanagisawa, Yukihiro Shimoi

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 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.

arXiv:cond-mat/9512160Dec 22, 19950 citations

Singlet ground state of the periodic Anderson model at half filling: A rigorous result

Kazuo Ueda, Hirokazu Tsunetsugu, Manfred Sigrist

Physical Review LettersFeb 17, 199293 citations

Spin correlations in dense Kondo systems

Paolo Maria Santini, Jenő Sólyom, Lucio Claudio Andreani +1 more

We performed numerical diagonalization studies of the periodic Anderson Model on finite chains up to 6 sites, in the integral valence limit for T=0. We find that in the weak coupling (Kondo) region the hybridization between f and conduction electrons induces pronounced correlations between the f spins. These correlations are ferromagnetic for low filling and become antiferromagnetic close to half-filling, with a smooth transition between the limiting cases. In no limit can the physics be completely described by a Ruderman–Kittel–Kasuya–Yosida effective spin Hamiltonian, as f and conduction band electrons are always correlated. To study the onset of long range order we considered also a simpler model for the half-filled case, called ‘‘Kondo necklace.’’ We studied the model at T=0 by numerical diagonalization and finite-size scaling, on chains up to 12 sites. We find that below a finite critical value of the Kondo coupling there exists a gapless phase with quasi long range antiferromagnetic correlations.We performed numerical diagonalization studies of the periodic Anderson Model on finite chains up to 6 sites, in the integral valence limit for T=0. We find that in the weak coupling (Kondo) region the hybridization between f and conduction electrons induces pronounced correlations between the f spins. These correlations are ferromagnetic for low filling and become antiferromagnetic close to half-filling, with a smooth transition between the limiting cases. In no limit can the physics be completely described by a Ruderman–Kittel–Kasuya–Yosida effective spin Hamiltonian, as f and conduction band electrons are always correlated. To study the onset of long range order we considered also a simpler model for the half-filled case, called ‘‘Kondo necklace.’’ We studied the model at T=0 by numerical diagonalization and finite-size scaling, on chains up to 12 sites. We find that below a finite critical value of the Kondo coupling there exists a gapless phase with quasi long range antiferromagnetic correlations.

Journal of Applied PhysicsMay 15, 19931 citation

Electric and magnetic properties of higher-spin Kondo-Heisenberg models at strong coupling

Riku Masui, Keisuke Totsuka

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.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.

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

Quantum Monte Carlo Simulations of the Half-Filled Two-Dimensional Kondo Lattice Model

Fakher F. Assaad

The 2D half-filled Kondo lattice model with exchange $J$ and nearest neighbor hopping $t$ is considered. It is shown that this model belongs to a class of Hamiltonians for which zero-temperature auxiliary field Monte Carlo methods may be efficiently applied. We compute the staggered moment and spin and quasiparticle gaps on lattice sizes up to $12\ifmmode\times\else\texttimes\fi{}12$. The competition between the RKKY interaction and Kondo effect leads to a continuous quantum phase transition between antiferromagnetic and spin-gapped insulators. This transition occurs at $J/t\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.45\ifmmode\pm\else\textpm\fi{}0.05$.The 2D half-filled Kondo lattice model with exchange $J$ and nearest neighbor hopping $t$ is considered. It is shown that this model belongs to a class of Hamiltonians for which zero-temperature auxiliary field Monte Carlo methods may be efficiently applied. We compute the staggered moment and spin and quasiparticle gaps on lattice sizes up to $12\ifmmode\times\else\texttimes\fi{}12$. The competition between the RKKY interaction and Kondo effect leads to a continuous quantum phase transition between antiferromagnetic and spin-gapped insulators. This transition occurs at $J/t\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.45\ifmmode\pm\else\textpm\fi{}0.05$.

arXiv:cond-mat/9904178Physical Review LettersJul 26, 1999134 citations

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 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 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.

The 2D half-filled Kondo lattice model with exchange

J

and nearest neighbor hopping

t

is considered. It is shown that this model belongs to a class of Hamiltonians for which zero-temperature auxiliary field Monte Carlo methods may be efficiently applied. We compute the staggered moment and spin and quasiparticle gaps on lattice sizes up to $12\ifmmode\times\else\texttimes\fi{}12$. The competition between the RKKY interaction and Kondo effect leads to a continuous quantum phase transition between antiferromagnetic and spin-gapped insulators. This transition occurs at $J/t\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.45\ifmmode\pm\else\textpm\fi{}0.05$.