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:cond-mat/0303159 · Physical review. B, Condensed matter

Ground-state properties of nanographite systems with zigzag edges

Toshiya Hikihara, Xiao Hu, Hsiu‐Hau Lin, Chung‐Yu Mou

Published Jul 30, 2003• 103 citations
arXivHTMLPDF

Abstract

A $\ensuremath{\pi}$-electron network in nanographite systems with zigzag edges exhibits strongly localized edge states, which are expected to have peculiar properties. We study effects of electron-electron interactions on ground-state properties of zigzag nanographite ribbons and open-ended zigzag nanotubes by means of the weak-coupling renormalization group and the density-matrix renormalization-group method. It is shown that the ground state is a spin-singlet Mott insulator with finite charge and spin gaps. We also find that the edge states are robust against the electronic correlations, resulting in edge-effective spins that can flip almost freely. The schematic picture for the low-energy physics of the systems is discussed.

DOI
10.1103/physrevb.68.035432

Related papers

Zigzag carbon nanotubes with generic electron-electron interactions

Judith E. Bunder, James Murray Hill

A Hamiltonian is derived for a zigzag carbon nanotube with an arbitrary number of weak electron-electron charge and spin interactions, which become significant in ultraclean systems. The renormalization group and bosonization are used to determine the ground-state phase diagram. Our phase diagram contains some exotic phases which have not previously been predicted in carbon nanotubes with physically possible interaction profiles. Phases of the undoped case include Mott insulators and a variety of density wave states. In the doped case a Tomanaga-Luttinger liquid is possible.

Physical Review B•Oct 6, 2009•5 citations

Quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons

Cornelie Koop, Stefan Weßel

We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic interedge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of the intraedge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the interedge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intraedge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intrachain couplings. The results for the critical exponents are compared also to several recent renormalization-group calculations for related long-ranged interacting quantum systems.

arXiv:1707.05522•Physical review. B./Physical review. B•Oct 9, 2017•16 citations

Entanglement, excitations, and correlation effects in narrow zigzag graphene nanoribbons

Imre Hagymási, Örs Legeza

We investigate the low-lying excitation spectrum and ground-state properties of narrow graphene nanoribbons with zigzag edge configurations. Nanoribbons of comparable widths have been synthesized very recently [P. Ruffieux et al., Nature (London) 531, 489 (2016)], and their descriptions require more sophisticated methods since in this regime conventional methods, like mean-field or density-functional theory with local-density approximation, fail to capture the enhanced quantum fluctuations. Using the unbiased density-matrix renormalization-group algorithm, we calculate the charge gaps with high accuracy for different widths and interaction strengths and compare them with mean-field results. It turns out that the gaps are much smaller in the former case due to the proper treatment of quantum fluctuations. Applying the elements of quantum information theory, we also reveal the entanglement structure inside a ribbon and examine the spectrum of subsystem density matrices to understand the origin of entanglement. We examine the possibility of magnetic ordering and the effect of magnetic field. Our findings are relevant for understanding the gap values in different recent experiments and the deviations between them.

arXiv:1605.03041•Physical review. B./Physical review. B•Oct 20, 2016•30 citations

Size dependence of excited state properties in zigzag graphene nanoribbons

Jessica Alfonsi

Density-matrix renormalization group results are reported for the excitonic transitions in zigzag graphene nanoribbons within the framework of the simple Hubbard model. This work shows that a one-dimensional quantum lattice model with open boundary conditions is able to capture the many-body features in the low-energy electronic spectra of these systems alongside the size dependence on the ribbon width. The obtained results agree with the trends of charge and spin excitation gaps available from quantum chemistry predictions.

Journal of Physics Conference Series•Dec 12, 2014•1 citation

Correlation effects in two-dimensional topological insulators

Yasuhiro Tada, Robert Peters, Masaki Oshikawa +3 more

We investigate correlation effects in two-dimensional topological insulators (TI). In the first part, we discuss finite size effects for interacting systems of different sizes in a ribbon geometry. For large systems, there are two pairs of well separated massless modes on both edges. For these systems, we analyze the finite size effects using a standard bosonization approach. For small systems, where the edge states are massive Dirac fermions, we use the inhomogeneous dynamical mean-field theory (DMFT) combined with iterative perturbation theory as an impurity solver to study interaction effects. We show that the finite size gap in the edge states is renormalized for weak interactions, which is consistent with a Fermi-liquid picture for small size TIs. In the second part, we investigate phase transitions in finite size TIs at zero temperature focusing on the effects of possible interedge umklapp scattering for the edge states within the inhomogeneous DMFT using the numerical renormalization group. We show that correlation effects are effectively stronger near the edge sites because the coordination number is smaller than in the bulk. Therefore the localization of the edge states around the edge sites, which is a fundamental property in TIs, is weakened for strong coupling strengths. However, we find no signs for ``edge Mott insulating states'' and the system stays in the topological insulating state, which is adiabatically connected to the noninteracting state for all interaction strengths smaller than the critical value. Increasing the interaction further, a nearly homogeneous Mott insulating state is stabilized.

arXiv:1202.3203•Physical Review B•Apr 23, 2012•73 citations

Entanglement and magnetism in high-spin graphene nanodisks

Imre Hagymási, Örs Legeza

We investigate the ground-state properties of triangular graphene nanoflakes with zigzag edge configurations. The description of zero-dimensional nanostructures requires accurate many-body techniques since the widely used density-functional theory with local density approximation or Hartree-Fock methods cannot handle the strong quantum fluctuations. Applying the unbiased density-matrix renormalization group algorithm we calculate the magnetization and entanglement patterns with high accuracy for different interaction strengths and compare them to the mean-field results. With the help of quantum information analysis and subsystem density matrices we reveal that the edges are strongly entangled with each other. We also address the effect of electron and hole doping and demonstrate that the magnetic properties of triangular nanoflakes can be controlled by an electric field, which reveals features of flat-band ferromagnetism. This may open up new avenues in graphene based spintronics.

arXiv:1711.05093•Physical review. B./Physical review. B•Jan 17, 2018•7 citations
A \ensuremathπ\ensuremath{\pi}\ensuremathπ-electron network in nanographite systems with zigzag edges exhibits strongly localized edge states, which are expected to have peculiar properties. We study effects of electron-electron interactions on ground-state properties of zigzag nanographite ribbons and open-ended zigzag nanotubes by means of the weak-coupling renormalization group and the density-matrix renormalization-group method. It is shown that the ground state is a spin-singlet Mott insulator with finite charge and spin gaps. We also find that the edge states are robust against the electronic correlations, resulting in edge-effective spins that can flip almost freely. The schematic picture for the low-energy physics of the systems is discussed.
A Hamiltonian is derived for a zigzag carbon nanotube with an arbitrary number of weak electron-electron charge and spin interactions, which become significant in ultraclean systems. The renormalization group and bosonization are used to determine the ground-state phase diagram. Our phase diagram contains some exotic phases which have not previously been predicted in carbon nanotubes with physically possible interaction profiles. Phases of the undoped case include Mott insulators and a variety of density wave states. In the doped case a Tomanaga-Luttinger liquid is possible.
We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic interedge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of the intraedge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the interedge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intraedge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intrachain couplings. The results for the critical exponents are compared also to several recent renormalization-group calculations for related long-ranged interacting quantum systems.
We investigate the low-lying excitation spectrum and ground-state properties of narrow graphene nanoribbons with zigzag edge configurations. Nanoribbons of comparable widths have been synthesized very recently [P. Ruffieux et al., Nature (London) 531, 489 (2016)], and their descriptions require more sophisticated methods since in this regime conventional methods, like mean-field or density-functional theory with local-density approximation, fail to capture the enhanced quantum fluctuations. Using the unbiased density-matrix renormalization-group algorithm, we calculate the charge gaps with high accuracy for different widths and interaction strengths and compare them with mean-field results. It turns out that the gaps are much smaller in the former case due to the proper treatment of quantum fluctuations. Applying the elements of quantum information theory, we also reveal the entanglement structure inside a ribbon and examine the spectrum of subsystem density matrices to understand the origin of entanglement. We examine the possibility of magnetic ordering and the effect of magnetic field. Our findings are relevant for understanding the gap values in different recent experiments and the deviations between them.
Density-matrix renormalization group results are reported for the excitonic transitions in zigzag graphene nanoribbons within the framework of the simple Hubbard model. This work shows that a one-dimensional quantum lattice model with open boundary conditions is able to capture the many-body features in the low-energy electronic spectra of these systems alongside the size dependence on the ribbon width. The obtained results agree with the trends of charge and spin excitation gaps available from quantum chemistry predictions.
We investigate correlation effects in two-dimensional topological insulators (TI). In the first part, we discuss finite size effects for interacting systems of different sizes in a ribbon geometry. For large systems, there are two pairs of well separated massless modes on both edges. For these systems, we analyze the finite size effects using a standard bosonization approach. For small systems, where the edge states are massive Dirac fermions, we use the inhomogeneous dynamical mean-field theory (DMFT) combined with iterative perturbation theory as an impurity solver to study interaction effects. We show that the finite size gap in the edge states is renormalized for weak interactions, which is consistent with a Fermi-liquid picture for small size TIs. In the second part, we investigate phase transitions in finite size TIs at zero temperature focusing on the effects of possible interedge umklapp scattering for the edge states within the inhomogeneous DMFT using the numerical renormalization group. We show that correlation effects are effectively stronger near the edge sites because the coordination number is smaller than in the bulk. Therefore the localization of the edge states around the edge sites, which is a fundamental property in TIs, is weakened for strong coupling strengths. However, we find no signs for ``edge Mott insulating states'' and the system stays in the topological insulating state, which is adiabatically connected to the noninteracting state for all interaction strengths smaller than the critical value. Increasing the interaction further, a nearly homogeneous Mott insulating state is stabilized.
We investigate the ground-state properties of triangular graphene nanoflakes with zigzag edge configurations. The description of zero-dimensional nanostructures requires accurate many-body techniques since the widely used density-functional theory with local density approximation or Hartree-Fock methods cannot handle the strong quantum fluctuations. Applying the unbiased density-matrix renormalization group algorithm we calculate the magnetization and entanglement patterns with high accuracy for different interaction strengths and compare them to the mean-field results. With the help of quantum information analysis and subsystem density matrices we reveal that the edges are strongly entangled with each other. We also address the effect of electron and hole doping and demonstrate that the magnetic properties of triangular nanoflakes can be controlled by an electric field, which reveals features of flat-band ferromagnetism. This may open up new avenues in graphene based spintronics.