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:1012.5163

Charge-density-wave and topological transitions in interacting Haldane model

Lei Wang, Hao Shi, Shiwei Zhang, Xiaoqun Wang, Xi Dai, Xiang Xie

Published Dec 23, 2010• 2 citations
arXivHTMLPDF

Abstract

Haldane model is a noninteracting model for spinless fermions showing nontrivial topological properties. Effect of the electron-electron interaction on the topological phase poses an intriguing question. By means of the Hartree-Fock mean field, the exact diagonalization and the constrained-path Monte Carlo methods we mapped out the phase diagram of the interacting Haldane model. It is found that interaction breaks down the topological phase and drives the system into the charge-density-wave state. Sequence of the two transitions depends on the strength of next-nearest-neighbor hopping. Many-body Chern number and the charge excitation gap are used to characterize the topological transition.

DOI
10.48550/arxiv.1012.5163

Related papers

Interaction effects and quantum phase transitions in topological insulators

Christopher N. Varney, Kai Sun, Marcos Rigol +1 more

We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at $T=0$ as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.

arXiv:1007.3502•Physical Review B•Sep 28, 2010•142 citations

Topological Phase Transitions in the Repulsively Interacting Haldane-Hubbard Model

Tuomas I. Vanhala, Topi Siro, Long Liang +3 more

Using dynamical mean-field theory and exact diagonalization we study the phase diagram of the repulsive Haldane-Hubbard model, varying the interaction strength and the sublattice potential difference. In addition to the quantum Hall phase with Chern number C=2 and the band insulator with C=0 present already in the noninteracting model, the system also exhibits a C=0 Mott insulating phase, and a C=1 quantum Hall phase. We explain the latter phase by a spontaneous symmetry breaking where one of the spin components is in the Hall state and the other in the band insulating state.

arXiv:1512.08804•Physical Review Letters•Jun 2, 2016•99 citations

Phase transitions in the Haldane-Hubbard model

Wan-Xiu He, Rubem Mondaini, Hong‐Gang Luo +2 more

The Haldane-Hubbard model is a prime example of the combined effects of band topology and electronic interaction. We revisit its spinful phase diagram at half filling as a consensus on the presence of SU(2) symmetry is currently lacking. To start, we utilize the Hartree-Fock mean-field method, which offers a direct understanding of symmetry breaking through the effective mass term that can acquire spin dependence. Our results, in agreement with previous studies, provide an instructive insight into the regime where the Chern number $C=1$, with only one spin species remaining topological. Besides that, we numerically study the phase diagram of the Haldane-Hubbard model via a large-scale infinite-density matrix renormalization group (iDMRG) method. The phase boundaries are determined by the Chern number and the correlation lengths obtained from the transfer-matrix spectrum. Unlike previous studies, the iDMRG method investigates the Haldane-Hubbard model on a thin and infinitely long cylinder and examines scenarios consistent with the two-dimensional thermodynamic limit. Here, the phase diagram we obtained qualitatively goes beyond the Hartree-Fock scope, particularly in the $C=1$ region, and serves as a quantitative benchmark for further theoretical and experimental investigations.

arXiv:2311.01821•Physical review. B./Physical review. B•Jan 12, 2024•16 citations

Photoinduced anomalous Hall effect in the interacting Haldane model: Targeting topological states with pump pulses

Can Shao, Pedro D Sacramento, Rubem Mondaini

We investigate the nonequilibrium dynamics of the spinless Haldane model with nearest-neighbor interactions on the honeycomb lattice by employing an unbiased numerical method. In this system, a first-order transition from the Chern insulator at weak coupling to the charge-density-wave (CDW) phase at strong coupling can be characterized by a level crossing of the lowest energy levels. Here we show that if adiabatically following the eigenstates across this level crossing, their Chern numbers are preserved, leading to the identification of a topologically nontrivial low-energy excited state in the CDW regime. By promoting a resonant energy excitation via an ultrafast circularly polarized pump pulse, we find that the system acquires a nonvanishing Hall response as a result of the large overlap enhancement between the time-dependent wave function and the topologically nontrivial excited state. This response is suggestive of a photoinduced topological phase transition via unitary dynamics, despite a proper definition of the Chern number remaining elusive for an out-of-equilibrium interacting system. We contrast these results with more common quench protocols in which such features are largely absent in the dynamics even if the postquench Hamiltonian displays a topologically nontrivial ground state.

arXiv:2105.01845•Physical review. B./Physical review. B•Sep 20, 2021•10 citations

Phase diagram of the interacting Haldane model with spin-dependent sublattice potentials

Can Shao, Hong‐Gang Luo

Using the exact-diagonalization (ED) and mean-field (MF) approaches, we investigate the ground-state phase diagram of the interacting Haldane model on the honeycomb lattice, incorporating spin-dependent sublattice potentials ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\sigma},\ensuremath{\alpha}}$. Here $\ensuremath{\alpha}=\text{A},\text{B}$ and $\ensuremath{\sigma}=\ensuremath{\uparrow},\ensuremath{\downarrow}$ denote the sublattice and spin components, respectively. Setting ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\sigma},\text{A}}=+\mathrm{\ensuremath{\Delta}}$ $(\ensuremath{-}\mathrm{\ensuremath{\Delta}})$ and ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\sigma},\text{B}}=\ensuremath{-}\mathrm{\ensuremath{\Delta}}$ $(+\mathrm{\ensuremath{\Delta}})$ for $\ensuremath{\sigma}=\ensuremath{\uparrow}$ $(\ensuremath{\downarrow})$ results in the system favoring a spin ordered state. Conversely, introducing the nearest-neighbor Coulomb interaction can induce charge ordering in the system. Due to the competition between these factors, we observe that in both ED and MF approaches, an exotic state with Chern number $C=1$ survives amidst two locally ordered phases and a topologically ordered phase with $C=2$. In the ED method, various properties, such as the fidelity metric, the excitation gaps and the structure factors, are employed to identify critical points. In the MF method, using a sufficiently large lattice size, we define the local order parameters and band gaps to characterize the phase transitions. The interacting Haldane model and the spin-dependent lattice potential may be experimentally realized in an ultracold atom gas, providing a potential means to detect this intriguing state.

arXiv:2401.17813•Physical review. B./Physical review. B•Jun 3, 2024•3 citations

Topological phase transition in the two-leg Hubbard model: Emergence of the Haldane phase via diagonal hopping and strong interactions

João Pedro Gama D'Elia, Thereza Paiva

We investigate the two-leg Hubbard model with diagonal hopping to explore the interplay between geometrical frustration and strong electron-electron interactions. Using the Density Matrix Renormalization Group (DMRG) method, we demonstrate the emergence of a topological Haldane phase, which results explicitly from the complementary effects of diagonal hopping-induced frustration and strong on-site Coulomb repulsion. The topological phase transition from a trivial insulator to the nontrivial Haldane phase is characterized by significant changes in magnetic properties, edge correlations, and the appearance of a nonzero string order parameter. Furthermore, we confirm the topological nature of this phase through a detailed analysis of the spin gap and entanglement spectrum, demonstrating clear signatures of symmetry-protected topological order.

arXiv:2504.02157•Physical review. B./Physical review. B•Jul 16, 2025•1 citation
Haldane model is a noninteracting model for spinless fermions showing nontrivial topological properties. Effect of the electron-electron interaction on the topological phase poses an intriguing question. By means of the Hartree-Fock mean field, the exact diagonalization and the constrained-path Monte Carlo methods we mapped out the phase diagram of the interacting Haldane model. It is found that interaction breaks down the topological phase and drives the system into the charge-density-wave state. Sequence of the two transitions depends on the strength of next-nearest-neighbor hopping. Many-body Chern number and the charge excitation gap are used to characterize the topological transition.
We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at T=0T=0T=0 as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.
Using dynamical mean-field theory and exact diagonalization we study the phase diagram of the repulsive Haldane-Hubbard model, varying the interaction strength and the sublattice potential difference. In addition to the quantum Hall phase with Chern number C=2 and the band insulator with C=0 present already in the noninteracting model, the system also exhibits a C=0 Mott insulating phase, and a C=1 quantum Hall phase. We explain the latter phase by a spontaneous symmetry breaking where one of the spin components is in the Hall state and the other in the band insulating state.
The Haldane-Hubbard model is a prime example of the combined effects of band topology and electronic interaction. We revisit its spinful phase diagram at half filling as a consensus on the presence of SU(2) symmetry is currently lacking. To start, we utilize the Hartree-Fock mean-field method, which offers a direct understanding of symmetry breaking through the effective mass term that can acquire spin dependence. Our results, in agreement with previous studies, provide an instructive insight into the regime where the Chern number C=1C=1C=1, with only one spin species remaining topological. Besides that, we numerically study the phase diagram of the Haldane-Hubbard model via a large-scale infinite-density matrix renormalization group (iDMRG) method. The phase boundaries are determined by the Chern number and the correlation lengths obtained from the transfer-matrix spectrum. Unlike previous studies, the iDMRG method investigates the Haldane-Hubbard model on a thin and infinitely long cylinder and examines scenarios consistent with the two-dimensional thermodynamic limit. Here, the phase diagram we obtained qualitatively goes beyond the Hartree-Fock scope, particularly in the C=1C=1C=1 region, and serves as a quantitative benchmark for further theoretical and experimental investigations.
We investigate the nonequilibrium dynamics of the spinless Haldane model with nearest-neighbor interactions on the honeycomb lattice by employing an unbiased numerical method. In this system, a first-order transition from the Chern insulator at weak coupling to the charge-density-wave (CDW) phase at strong coupling can be characterized by a level crossing of the lowest energy levels. Here we show that if adiabatically following the eigenstates across this level crossing, their Chern numbers are preserved, leading to the identification of a topologically nontrivial low-energy excited state in the CDW regime. By promoting a resonant energy excitation via an ultrafast circularly polarized pump pulse, we find that the system acquires a nonvanishing Hall response as a result of the large overlap enhancement between the time-dependent wave function and the topologically nontrivial excited state. This response is suggestive of a photoinduced topological phase transition via unitary dynamics, despite a proper definition of the Chern number remaining elusive for an out-of-equilibrium interacting system. We contrast these results with more common quench protocols in which such features are largely absent in the dynamics even if the postquench Hamiltonian displays a topologically nontrivial ground state.
Using the exact-diagonalization (ED) and mean-field (MF) approaches, we investigate the ground-state phase diagram of the interacting Haldane model on the honeycomb lattice, incorporating spin-dependent sublattice potentials ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\sigma},\ensuremath{\alpha}}$. Here $\ensuremath{\alpha}=\text{A},\text{B}$ and $\ensuremath{\sigma}=\ensuremath{\uparrow},\ensuremath{\downarrow}$ denote the sublattice and spin components, respectively. Setting ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\sigma},\text{A}}=+\mathrm{\ensuremath{\Delta}}$ $(\ensuremath{-}\mathrm{\ensuremath{\Delta}})$ and ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\sigma},\text{B}}=\ensuremath{-}\mathrm{\ensuremath{\Delta}}$ $(+\mathrm{\ensuremath{\Delta}})$ for $\ensuremath{\sigma}=\ensuremath{\uparrow}$ $(\ensuremath{\downarrow})$ results in the system favoring a spin ordered state. Conversely, introducing the nearest-neighbor Coulomb interaction can induce charge ordering in the system. Due to the competition between these factors, we observe that in both ED and MF approaches, an exotic state with Chern number C=1C=1C=1 survives amidst two locally ordered phases and a topologically ordered phase with C=2C=2C=2. In the ED method, various properties, such as the fidelity metric, the excitation gaps and the structure factors, are employed to identify critical points. In the MF method, using a sufficiently large lattice size, we define the local order parameters and band gaps to characterize the phase transitions. The interacting Haldane model and the spin-dependent lattice potential may be experimentally realized in an ultracold atom gas, providing a potential means to detect this intriguing state.
We investigate the two-leg Hubbard model with diagonal hopping to explore the interplay between geometrical frustration and strong electron-electron interactions. Using the Density Matrix Renormalization Group (DMRG) method, we demonstrate the emergence of a topological Haldane phase, which results explicitly from the complementary effects of diagonal hopping-induced frustration and strong on-site Coulomb repulsion. The topological phase transition from a trivial insulator to the nontrivial Haldane phase is characterized by significant changes in magnetic properties, edge correlations, and the appearance of a nonzero string order parameter. Furthermore, we confirm the topological nature of this phase through a detailed analysis of the spin gap and entanglement spectrum, demonstrating clear signatures of symmetry-protected topological order.