Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

General result on charged and spin-excitation gaps in strongly correlated electron systems at half filling

Guang-Shan Tian, Lei‐Han Tang

Published Oct 15, 1999• 6 citations
Publisher

Abstract

The relationship between charged and spin-excitation gaps of the half-filled Hubbard model, the symmetric periodic Anderson model, and the Kondo lattice model is considered for a general $d$-dimensional bipartite lattice. In a previous paper [G. S. Tian, Phys. Rev. B 58, 7612 (1998)], it was shown that the quasiparticle gaps of these models at half filling are always larger than their spin excitation gaps. In the present paper, we establish a theorem, which states that the charged gap is also greater than the corresponding spin gap in these models. This conclusion, which has been reached previously for one-dimensional systems based on variational and the density-matrix renormalization-group numerical calculations, is thus put on a rigorous and more general footing.

DOI
10.1103/physrevb.60.11336

Related papers

Charged and spin-excitation gaps in half-filled strongly correlated electron systems: A rigorous result

Guang-Shan Tian

By exploiting the particle-hole symmetries of the Hubbard model, the periodic Anderson model, and the Kondo lattice model at half-filling and by applying a generalized version of Lieb's spin-reflection positivity method, we show that the charged gaps of these models are always larger than their spin-excitation gaps. This theorem confirms the previous results derived by either the variational approach or the density-matrix renormalization-group approach.

arXiv:cond-mat/9807272•Physical review. B, Condensed matter•Sep 15, 1998•14 citations

Kondo insulators modeled by the one-dimensional Anderson lattice: A numerical-renormalization-group study

M. Guerrero, Clare C. Yu

In order to better understand Kondo insulators, we have studied both the symmetric and asymmetric Anderson lattices at half filling in one dimension using the density-matrix formulation of the numerical renormalization group. The asymmetric case is treated in the mixed-valence regime. We have calculated the charge gap, the spin gap, and the quasiparticle gap as a function of the repulsive interaction U using open boundary conditions for lattices as large as 24 sites. We find that the charge gap is larger than the spin gap for all U for both the symmetric and asymmetric cases. Ruderman-Kittel-Kasuya-Yosida interactions are evident in the f-spin--f-spin correlation functions at large U in the symmetric case, but are suppressed in the asymmetric case as the f level approaches the Fermi energy. This suppression can also be seen in the staggered susceptibility \ensuremath{\chi}(q=2${\mathit{k}}_{\mathit{F}}$) and it is consistent with neutron scattering measurements of \ensuremath{\chi}(q) in CeNiSn.

arXiv:cond-mat/9503006•Physical review. B, Condensed matter•Apr 15, 1995•40 citations

Antiferromagnetic correlation in the half-filled strongly correlated electron models at nonzero temperature: A rigorous result

Guang-Shan Tian

As an extension of our previous rigorous investigation on the spin correlations in the ground states of the half-filled Hubbard model and the periodic Anderson model [G. S. Tian, Phys. Rev. B 50, 6246 (1994)], in the present paper we study the behavior of these correlation functions at finite temperature. We show rigorously that, at any $T\ensuremath{\ne}0,$ the predominant spin correlations in these systems are antiferromagnetic. Furthermore, based on this result, we also show that a quasi-one (or two)-dimensional itinerant electron ferrimagnet must have a gapless branch of ferromagnetic excitations. This conclusion is consistent with the previous results derived by the spin-wave theory.

Physical review. B, Condensed matter•May 22, 2001•9 citations

A rigorous study on the charged gap in strongly correlated electron clusters

Guang-Shan Tian, Jigang Wang

In this paper, we study a revised definition c of the charged gap for the strongly correlated electron models on small clusters, proposed by Nishino, in a mathematically rigorous way. By applying a simplified version of Lieb's spin-reflection-positivity method, we show that this quantity is always positive for the half-filled Hubbard model, the periodic Anderson model and the Kondo lattice model. We also establish a model-dependent lower bound to the charged gap. Our results show explicitly the role played by electron repulsion in opening up a nonvanishing charged gap of a cluster.

Journal of Physics A Mathematical and General•Jan 21, 2002•2 citations

Phase transition in the one-dimensional Kondo lattice model with attractive electron-electron interaction

Naokazu Shibata, Manfred Sigrist, Elmar Heeb

The one-dimensional Kondo lattice model with attractive interaction among the conduction electrons is analyzed in the case of half-filling. It is shown that there are three distinct phases depending on the coupling constants of the model. Two phases have a spin and charge gap. While one shows a clear distinction of the spin and charge excitation spectrum the other phase may be characterized as a band insulator type where both excitations are due to two-particle states. The third phase is gapless in both channels and has quasi-long-range order in the spin- and charge-density-wave correlation. In this phase the spin and charge excitations have a clearly separated spectrum. For the analysis we discuss first two limiting cases. Then a density matrix renormalization group calculation on finite systems is applied to determine the phase diagram and the correlation functions in the gapped and gapless phase for general coupling constants.

arXiv:cond-mat/9704226•Physical review. B, Condensed matter•Nov 1, 1997•1 citation

Interorbital interaction in the one-dimensional periodic Anderson model: Density matrix renormalization group study

Imre Hagymási, Jenő Sólyom, Örs Legeza

We investigate the effect of the Coulomb interaction, ${U}_{cf}$, between the conduction and $f$ electrons in the periodic Anderson model using the density matrix renormalization group algorithm. We calculate the excitation spectrum of the half-filled symmetric model with an emphasis on the spin and charge excitations. In the one-dimensional version of the model, it is found that the spin gap is smaller than the charge gap below a certain value of ${U}_{cf}$ and the reversed inequality is valid for stronger ${U}_{cf}$. This behavior is also verified by the behavior of the spin and density correlation functions. We also perform a quantum information analysis of the model and determine the entanglement map of the $f$ and conduction electrons. It is revealed that for a certain ${U}_{cf}$ the ground state is dominated by the configuration in which the conduction and $f$ electrons are strongly entangled, and the ground state is almost a product state. For larger ${U}_{cf}$, the sites are occupied alternatingly dominantly by two $f$ electrons or by two conduction electrons.

arXiv:1406.6292•Physical Review B•Sep 22, 2014•7 citations
The relationship between charged and spin-excitation gaps of the half-filled Hubbard model, the symmetric periodic Anderson model, and the Kondo lattice model is considered for a general ddd-dimensional bipartite lattice. In a previous paper [G. S. Tian, Phys. Rev. B 58, 7612 (1998)], it was shown that the quasiparticle gaps of these models at half filling are always larger than their spin excitation gaps. In the present paper, we establish a theorem, which states that the charged gap is also greater than the corresponding spin gap in these models. This conclusion, which has been reached previously for one-dimensional systems based on variational and the density-matrix renormalization-group numerical calculations, is thus put on a rigorous and more general footing.
In order to better understand Kondo insulators, we have studied both the symmetric and asymmetric Anderson lattices at half filling in one dimension using the density-matrix formulation of the numerical renormalization group. The asymmetric case is treated in the mixed-valence regime. We have calculated the charge gap, the spin gap, and the quasiparticle gap as a function of the repulsive interaction U using open boundary conditions for lattices as large as 24 sites. We find that the charge gap is larger than the spin gap for all U for both the symmetric and asymmetric cases. Ruderman-Kittel-Kasuya-Yosida interactions are evident in the f-spin--f-spin correlation functions at large U in the symmetric case, but are suppressed in the asymmetric case as the f level approaches the Fermi energy. This suppression can also be seen in the staggered susceptibility \ensuremath{\chi}(q=2kF{\mathit{k}}_{\mathit{F}}kF​) and it is consistent with neutron scattering measurements of \ensuremath{\chi}(q) in CeNiSn.
As an extension of our previous rigorous investigation on the spin correlations in the ground states of the half-filled Hubbard model and the periodic Anderson model [G. S. Tian, Phys. Rev. B 50, 6246 (1994)], in the present paper we study the behavior of these correlation functions at finite temperature. We show rigorously that, at any $T\ensuremath{\ne}0,$ the predominant spin correlations in these systems are antiferromagnetic. Furthermore, based on this result, we also show that a quasi-one (or two)-dimensional itinerant electron ferrimagnet must have a gapless branch of ferromagnetic excitations. This conclusion is consistent with the previous results derived by the spin-wave theory.
In this paper, we study a revised definition c of the charged gap for the strongly correlated electron models on small clusters, proposed by Nishino, in a mathematically rigorous way. By applying a simplified version of Lieb's spin-reflection-positivity method, we show that this quantity is always positive for the half-filled Hubbard model, the periodic Anderson model and the Kondo lattice model. We also establish a model-dependent lower bound to the charged gap. Our results show explicitly the role played by electron repulsion in opening up a nonvanishing charged gap of a cluster.
The one-dimensional Kondo lattice model with attractive interaction among the conduction electrons is analyzed in the case of half-filling. It is shown that there are three distinct phases depending on the coupling constants of the model. Two phases have a spin and charge gap. While one shows a clear distinction of the spin and charge excitation spectrum the other phase may be characterized as a band insulator type where both excitations are due to two-particle states. The third phase is gapless in both channels and has quasi-long-range order in the spin- and charge-density-wave correlation. In this phase the spin and charge excitations have a clearly separated spectrum. For the analysis we discuss first two limiting cases. Then a density matrix renormalization group calculation on finite systems is applied to determine the phase diagram and the correlation functions in the gapped and gapless phase for general coupling constants.
We investigate the effect of the Coulomb interaction, Ucf{U}_{cf}Ucf​, between the conduction and fff electrons in the periodic Anderson model using the density matrix renormalization group algorithm. We calculate the excitation spectrum of the half-filled symmetric model with an emphasis on the spin and charge excitations. In the one-dimensional version of the model, it is found that the spin gap is smaller than the charge gap below a certain value of Ucf{U}_{cf}Ucf​ and the reversed inequality is valid for stronger Ucf{U}_{cf}Ucf​. This behavior is also verified by the behavior of the spin and density correlation functions. We also perform a quantum information analysis of the model and determine the entanglement map of the fff and conduction electrons. It is revealed that for a certain Ucf{U}_{cf}Ucf​ the ground state is dominated by the configuration in which the conduction and fff electrons are strongly entangled, and the ground state is almost a product state. For larger Ucf{U}_{cf}Ucf​, the sites are occupied alternatingly dominantly by two fff electrons or by two conduction electrons.