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

arXiv:0809.3235 · Physical Review B

One-dimensional Kondo lattice model at quarter filling

J. C. Xavier, E. Miranda

Published Oct 8, 2008• 8 citations
arXivHTMLPDF

Abstract

We revisit the problem of the quarter-filled one-dimensional Kondo lattice model, for which the existence of a dimerized phase and a nonzero charge gap had been reported by Xavier et al. [Phys. Rev. Lett. 90, 247204 (2003)]. Recently, some objections were raised claiming that the system is neither dimerized nor has a charge gap. In the interest of clarifying this important issue, we show that these objections are based on results obtained under conditions in which the dimer order is artificially suppressed. We use the incontrovertible dimerized phase of the Majumdar-Ghosh point of the ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model as a paradigm with which to illustrate this artificial suppression. Finally, by means of extremely accurate density-matrix renormalization-group calculations, we show that the charge gap is indeed nonzero in the dimerized phase.

DOI
10.1103/physrevb.78.144406

Related papers

Comments on "Dimerization Induced by the RKKY Interaction"

Naokazu Shibata, Chisa Hotta

Recently, Xavier et al. claimed the existence of an insulating spin dimer state in the one-dimensional Kondo lattice model at quarter-filling amidst the paramagnetic metallic phase. In this comment we show that the dimer-dimer correlation decays algebraically at long distances and the charge gap vanishes in the bulk limit.

arXiv:cond-mat/0503476•Mar 18, 2005•0 citations

Coupled dimer and bond-order-wave order in the quarter-filled one-dimensional Kondo lattice model

Yixuan Huang, D. N. Sheng, C. S. Ting

Motivated by experiments on the organic compound ${(\text{Per})}_{2}[\text{Pt}{(\text{mnt})}_{2}]$, we study the ground state of the one-dimensional Kondo lattice model at quarter filling with the density matrix renormalization group method. We show a coupled dimer and bond-order-wave (BOW) state in the weak-coupling regime for the localized spins and itinerant electrons, respectively. The quantum phase transitions for the dimer and the BOW orders occur at the same critical coupling parameter ${J}_{c}$, with the opening of a charge gap. The emergence of the combination of dimer and BOW order agrees with the experimental findings of the simultaneous Peierls and spin-Peierls transitions at low temperatures, which provides a theoretical understanding of such a phase transition. We also show that the localized spins in this insulating state have quasi-long-ranged spin correlations with collinear configurations, which resemble the classical dimer order in the absence of a magnetic order.

arXiv:2009.13089•Physical review. B./Physical review. B•Dec 24, 2020•5 citations

Dimensionality Effects on the Charge Gap in the Dimerized Hubbard Model at Quarter Filling: the Density-Matrix and Perturbative Renormalization-Group Approaches

Kenji Yonemitsu, Jun‐ichiro Kishine

We study dimensionality effects on the charge gap in the dimerized Hubbard model at quarter filling, with two approaches. First, we examine three chains coupled via the interchain one-particle hopping integral t b , by the density-matrix renormalization-group (DMRG) method. Next, we consider the d =1+ε dimensional model, using the perturbative renormalization-group (PRG) method. The dimensionality is controlled through t b and ε, respectively. Both approaches lead to the conclusion that, for a finite dimerization ratio, the charge gap decreases as the dimensionality increases.

Journal of the Physical Society of Japan•Jul 15, 2000•3 citations

Interplay of Lattice Dimerization and Charge Ordering in One-Dimensional Quarter-Filled Electron Systems

Muneo Sugiura, Masahisa Tsuchiizu, Yoshikazu Suzumura

The effect of charge ordering on lattice dimerization has been investigated in the one-dimensional extended Peierls–Hubbard model at quarter filling. We estimate the strength of the lattice dimerization by applying the bosonization method and the perturbative renormalization-group method. In the ground state, it is shown that a first-order phase transition takes place between the dimerized insulator and the charge-ordered insulator. The lattice dimerization disappears in the charge-ordered state, while the lattice dimerization is appreciably suppressed even in the dimerized insulating state due to charge fluctuations. The phase diagram at finite temperature is also discussed.

Journal of the Physical Society of Japan•Sep 15, 2004•8 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

Dimerization and incommensurate spiral spin correlations in the zigzag spin chain: Analogies to the Kondo lattice

Steven R. White, Ian K. Affleck

Using the density matrix renormalization group and a bosonization approach, we study a spin-1/2 antiferromagnetic Heisenberg chain with near-neighbor coupling ${\mathit{J}}_{1}$ and frustrating second-neighbor coupling ${\mathit{J}}_{2}$, particularly in the limit ${\mathit{J}}_{2}$\ensuremath{\gg}${\mathit{J}}_{1}$. This system exhibits both dimerization and incommensurate spiral spin correlations. We argue that this system is closely related to a doped, spin-gapped phase of the one-dimensional Kondo lattice. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9602126•Physical review. B, Condensed matter•Oct 1, 1996•548 citations
We revisit the problem of the quarter-filled one-dimensional Kondo lattice model, for which the existence of a dimerized phase and a nonzero charge gap had been reported by Xavier et al. [Phys. Rev. Lett. 90, 247204 (2003)]. Recently, some objections were raised claiming that the system is neither dimerized nor has a charge gap. In the interest of clarifying this important issue, we show that these objections are based on results obtained under conditions in which the dimer order is artificially suppressed. We use the incontrovertible dimerized phase of the Majumdar-Ghosh point of the J1\ensuremath−J2{J}_{1}\ensuremath{-}{J}_{2}J1​\ensuremath−J2​ Heisenberg model as a paradigm with which to illustrate this artificial suppression. Finally, by means of extremely accurate density-matrix renormalization-group calculations, we show that the charge gap is indeed nonzero in the dimerized phase.
Motivated by experiments on the organic compound (Per)2[Pt(mnt)2]{(\text{Per})}_{2}[\text{Pt}{(\text{mnt})}_{2}](Per)2​[Pt(mnt)2​], we study the ground state of the one-dimensional Kondo lattice model at quarter filling with the density matrix renormalization group method. We show a coupled dimer and bond-order-wave (BOW) state in the weak-coupling regime for the localized spins and itinerant electrons, respectively. The quantum phase transitions for the dimer and the BOW orders occur at the same critical coupling parameter Jc{J}_{c}Jc​, with the opening of a charge gap. The emergence of the combination of dimer and BOW order agrees with the experimental findings of the simultaneous Peierls and spin-Peierls transitions at low temperatures, which provides a theoretical understanding of such a phase transition. We also show that the localized spins in this insulating state have quasi-long-ranged spin correlations with collinear configurations, which resemble the classical dimer order in the absence of a magnetic order.
We study dimensionality effects on the charge gap in the dimerized Hubbard model at quarter filling, with two approaches. First, we examine three chains coupled via the interchain one-particle hopping integral t b , by the density-matrix renormalization-group (DMRG) method. Next, we consider the d =1+ε dimensional model, using the perturbative renormalization-group (PRG) method. The dimensionality is controlled through t b and ε, respectively. Both approaches lead to the conclusion that, for a finite dimerization ratio, the charge gap decreases as the dimensionality increases.
The effect of charge ordering on lattice dimerization has been investigated in the one-dimensional extended Peierls–Hubbard model at quarter filling. We estimate the strength of the lattice dimerization by applying the bosonization method and the perturbative renormalization-group method. In the ground state, it is shown that a first-order phase transition takes place between the dimerized insulator and the charge-ordered insulator. The lattice dimerization disappears in the charge-ordered state, while the lattice dimerization is appreciably suppressed even in the dimerized insulating state due to charge fluctuations. The phase diagram at finite temperature is also discussed.
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.
Using the density matrix renormalization group and a bosonization approach, we study a spin-1/2 antiferromagnetic Heisenberg chain with near-neighbor coupling J1{\mathit{J}}_{1}J1​ and frustrating second-neighbor coupling J2{\mathit{J}}_{2}J2​, particularly in the limit J2{\mathit{J}}_{2}J2​\ensuremath{\gg}J1{\mathit{J}}_{1}J1​. This system exhibits both dimerization and incommensurate spiral spin correlations. We argue that this system is closely related to a doped, spin-gapped phase of the one-dimensional Kondo lattice. \textcopyright{} 1996 The American Physical Society.