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:1805.01116 · Physical review. B./Physical review. B

Quantum anomalous Hall insulator stabilized by competing interactions

Shouvik Sur, Shou-Shu Gong, Kun Yang, Oskar Vafek

Published Sep 26, 2018• 28 citations
arXivHTMLPDF

Abstract

We study the quantum phases driven by interaction in a semimetal with a quadratic band touching at the Fermi level. By combining the density matrix renormalization group (DMRG), analytical power expanded Gibbs potential method, and the weak coupling renormalization group, we study a spinless fermion system on a checkerboard lattice at half-filling, which has a quadratic band touching in the absence of interaction. In the presence of strong nearest-neighbor (${V}_{1}$) and next-nearest-neighbor (${V}_{2}$) interactions, we identify a site nematic insulator phase, a stripe insulator phase, and a phase separation region, in agreement with the phase diagram obtained analytically in the strong coupling limit (i.e., in the absence of fermion hopping). In the intermediate interaction regime we establish a quantum anomalous Hall phase in the DMRG as evidenced by the spontaneous time-reversal symmetry breaking and the appearance of a quantized Chern number $C=1$. For weak interaction we utilize the power expanded Gibbs potential method that treats ${V}_{1}$ and ${V}_{2}$ on equal footing, as well as the weak coupling renormalization group. Our analytical results reveal that not only the repulsive ${V}_{1}$ interaction, but also the ${V}_{2}$ interaction (both repulsive and attractive), can drive the quantum anomalous Hall phase. We also determine the phase boundary in the ${V}_{1}\text{\ensuremath{-}}{V}_{2}$ plane that separates the semimetal from the quantum anomalous Hall state. Finally, we show that the nematic semimetal, which was proposed for $|{V}_{2}|\ensuremath{\gg}{V}_{1}$ at weak coupling in a previous study, is absent, and the quantum anomalous Hall state is the only weak coupling instability of the spinless quadratic band touching semimetal.

DOI
10.1103/physrevb.98.125144

Related papers

Interaction-driven quantum anomalous Hall insulator in a Dirac semimetal

Hongyu Lu, Shouvik Sur, Shou-Shu Gong +1 more

The interaction-driven quantum anomalous Hall (QAH) insulator has been sought for a long time in a Dirac semimetal with linear band touching points at the Fermi level. By combining exact diagonalization, density matrix renormalization group, and analytical methods, we study a spinless fermion system on the checkerboard lattice with twofold rotational symmetry, which realizes two Dirac band touching points in the absence of interaction. At weak coupling, the Dirac semimetal is stable. At a finite density-density repulsive interaction, we analyze possible symmetry broken states, and find that an QAH state is stabilized when the interaction strength exceeds the energy scale controlling the separation between the Dirac points. Through numerical simulations, we verify the existence of the QAH phase with spontaneous time-reversal symmetry breaking and quantized Chern number $C=1$.

arXiv:2110.03059•Physical review. B./Physical review. B•Nov 3, 2022•9 citations

Tuning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems

Tian-Sheng Zeng, Wei Zhu, Donna Sheng

Abstract Interaction-driven topological phases significantly enrich the class of topological materials and thus are of great importance. Here, we study the phase diagram of interacting spinless fermions filling the two-dimensional checkerboard lattice with a quadratic band touching (QBT) point. By developing new diagnosis based on the state-of-the-art density-matrix renormalization group and exact diagonalization, we determine accurate quantum phase diagram for such a system at half-filling with three distinct phases. For weak nearest-neighboring interactions, we demonstrate the instability of the QBT towards an interaction-driven spontaneous quantum anomalous Hall (QAH) effect. For strong interactions, the system breaks the rotational symmetry realizing a nematic charge-density-wave (CDW) phase. Interestingly, for intermediate interactions we discover a symmetry-broken bond-ordered critical phase sandwiched in between the QAH and CDW phases, which splits the QBT into two Dirac points driven by interaction. Instead of the direct transition between QAH and CDW phases, our identification of an intermediate phase sheds new light on the theoretical understanding of the interaction-driven phases in QBT systems.

arXiv:1805.01101•npj Quantum Materials•Sep 17, 2018•38 citations

Quantum anomalous Hall phase stabilized via realistic interactions on a kagome lattice

Yafei Ren, Tian-Sheng Zeng, W. Zhu +1 more

We study the quantum phases of spinless fermions at one-third filling on a kagome lattice featuring a quadratic band touching Fermi point. In the presence of weak first and second nearest-neighbor repulsive interactions (${V}_{1}$ and ${V}_{2}$), we demonstrate an interaction driven quantum anomalous Hall effect by employing exact diagonalization and density-matrix renormalization group methods. The time-reversal symmetry is broken spontaneously by forming loop currents that exhibit long-range correlation. Quantized Hall conductance corresponding to a Chern number of $\ifmmode\pm\else\textpm\fi{}1$ is obtained by measuring the pumped charge through inserting flux in a cylinder geometry. We find that the energy gap, which topologically protects the emerging ground states, can be enhanced remarkably by a moderate ${V}_{2}<{V}_{1}$ via calculating the spectrum and charge excitation gaps, which highlights the experimentally feasible scheme of realizing the interaction driven topological phase by spatially decaying interactions on topologically trivial lattice models.

arXiv:1806.11094•Physical review. B./Physical review. B•Nov 26, 2018•16 citations

Interaction-induced nematic Dirac semimetal from quadratic band touching: A constrained-path quantum Monte Carlo study

Zi Hong Liu, Hongyu Lu, Zi Yang Meng +1 more

Electronic systems with quadratic band touchings, commonly found in two- and three-dimensional materials such as Bernal-stacked bilayer graphene, kagome metals, HgTe, and pyrochlore iridates, have attracted significant interest concerning the role of interactions in shaping their electronic properties. However, even in the simplest model of spinless fermions on a two-dimensional checkerboard lattice, the quantum phase diagram as a function of nearest-neighbor interaction remains under debate. We employ constrained-path quantum Monte Carlo simulations (CP-QMC) simulations to investigate the problem using a two-dimensional torus geometry. We cross-validate our results on small lattices by comparing them with density-matrix renormalization group calculations, finding quantitative agreement. In particular, we implement an improved optimization scheme within the CP-QMC simulations, enabling the identification of a bond-nematic Dirac semimetal phase that was found in tensor-network studies on cylindrical geometries, but remains inaccessible to Hartree-Fock mean-field methods. The CP-QMC approach makes it possible to establish the emergence of this phase in a geometry that preserves lattice rotational symmetry and permits extrapolation to the thermodynamic limit. Our results show that the quantum phase diagram of spinless fermions on the checkerboard lattice with nearest-neighbor repulsion features three interaction-induced phases at half filling: a quantum anomalous Hall insulator at weak coupling, a bond-nematic Dirac semimetal at intermediate coupling, and a site-nematic insulator at strong coupling.

arXiv:2507.15668•SciPost Physics•Jun 26, 2026•0 citations

Quantum anomalous Hall domains in a quenched topological Mott insulator

Lara Ulčakar, G. Lemut, Tomaž Rejec +1 more

We study an interacting spinless quadratic band touching model that realizes a topological Mott insulating state. We quench the interaction from a value corresponding to the nematic insulator to that of the quantum anomalous Hall (QAH) ordered phase. We perform time-dependent Hartree-Fock simulations and show that after the quench the system realizes an excited Dirac semimetal state, which is, however, unstable and spontaneously evolves to a state with inhomogeneous nematic and QAH order parameters. The modulations form a stripe pattern that grows exponentially with time until the local Chern marker reaches unity. The alternating QAH order defines a domain structure with boundaries that host chiral sublattice currents.

Physical review. B./Physical review. B•May 20, 2025•1 citation

Quantum anomalous Hall domains in a Quenched Topological Mott Insulator

Lara Ulčakar, G. Lemut, Tomaž Rejec +1 more

We study an interacting spinless quadratic band touching model that realizes a topological Mott insulating state. We quench the interaction from a value corresponding to the nematic insulator to that of the quantum anomalous Hall (QAH) ordered phase. We perform time-dependent Hartree-Fock simulations and show that after the quench the system realizes an excited Dirac semimetal state, which is however unstable and spontaneously evolves to a state with inhomogeneous nematic and QAH order parameters. The modulations form a stripe pattern that grows exponentially with time until the local Chern marker reaches unity. The alternating QAH order defines a domain structure with boundaries that host chiral sublattice currents.

arXiv:2502.05035•Feb 7, 2025•0 citations
We study the quantum phases driven by interaction in a semimetal with a quadratic band touching at the Fermi level. By combining the density matrix renormalization group (DMRG), analytical power expanded Gibbs potential method, and the weak coupling renormalization group, we study a spinless fermion system on a checkerboard lattice at half-filling, which has a quadratic band touching in the absence of interaction. In the presence of strong nearest-neighbor (V1{V}_{1}V1​) and next-nearest-neighbor (V2{V}_{2}V2​) interactions, we identify a site nematic insulator phase, a stripe insulator phase, and a phase separation region, in agreement with the phase diagram obtained analytically in the strong coupling limit (i.e., in the absence of fermion hopping). In the intermediate interaction regime we establish a quantum anomalous Hall phase in the DMRG as evidenced by the spontaneous time-reversal symmetry breaking and the appearance of a quantized Chern number C=1C=1C=1. For weak interaction we utilize the power expanded Gibbs potential method that treats V1{V}_{1}V1​ and V2{V}_{2}V2​ on equal footing, as well as the weak coupling renormalization group. Our analytical results reveal that not only the repulsive V1{V}_{1}V1​ interaction, but also the V2{V}_{2}V2​ interaction (both repulsive and attractive), can drive the quantum anomalous Hall phase. We also determine the phase boundary in the V1\ensuremath-V2{V}_{1}\text{\ensuremath{-}}{V}_{2}V1​\ensuremath-V2​ plane that separates the semimetal from the quantum anomalous Hall state. Finally, we show that the nematic semimetal, which was proposed for ∣V2∣\ensuremath≫V1|{V}_{2}|\ensuremath{\gg}{V}_{1}∣V2​∣\ensuremath≫V1​ at weak coupling in a previous study, is absent, and the quantum anomalous Hall state is the only weak coupling instability of the spinless quadratic band touching semimetal.
The interaction-driven quantum anomalous Hall (QAH) insulator has been sought for a long time in a Dirac semimetal with linear band touching points at the Fermi level. By combining exact diagonalization, density matrix renormalization group, and analytical methods, we study a spinless fermion system on the checkerboard lattice with twofold rotational symmetry, which realizes two Dirac band touching points in the absence of interaction. At weak coupling, the Dirac semimetal is stable. At a finite density-density repulsive interaction, we analyze possible symmetry broken states, and find that an QAH state is stabilized when the interaction strength exceeds the energy scale controlling the separation between the Dirac points. Through numerical simulations, we verify the existence of the QAH phase with spontaneous time-reversal symmetry breaking and quantized Chern number C=1C=1C=1.
Abstract Interaction-driven topological phases significantly enrich the class of topological materials and thus are of great importance. Here, we study the phase diagram of interacting spinless fermions filling the two-dimensional checkerboard lattice with a quadratic band touching (QBT) point. By developing new diagnosis based on the state-of-the-art density-matrix renormalization group and exact diagonalization, we determine accurate quantum phase diagram for such a system at half-filling with three distinct phases. For weak nearest-neighboring interactions, we demonstrate the instability of the QBT towards an interaction-driven spontaneous quantum anomalous Hall (QAH) effect. For strong interactions, the system breaks the rotational symmetry realizing a nematic charge-density-wave (CDW) phase. Interestingly, for intermediate interactions we discover a symmetry-broken bond-ordered critical phase sandwiched in between the QAH and CDW phases, which splits the QBT into two Dirac points driven by interaction. Instead of the direct transition between QAH and CDW phases, our identification of an intermediate phase sheds new light on the theoretical understanding of the interaction-driven phases in QBT systems.
We study the quantum phases of spinless fermions at one-third filling on a kagome lattice featuring a quadratic band touching Fermi point. In the presence of weak first and second nearest-neighbor repulsive interactions (V1{V}_{1}V1​ and V2{V}_{2}V2​), we demonstrate an interaction driven quantum anomalous Hall effect by employing exact diagonalization and density-matrix renormalization group methods. The time-reversal symmetry is broken spontaneously by forming loop currents that exhibit long-range correlation. Quantized Hall conductance corresponding to a Chern number of $\ifmmode\pm\else\textpm\fi{}1$ is obtained by measuring the pumped charge through inserting flux in a cylinder geometry. We find that the energy gap, which topologically protects the emerging ground states, can be enhanced remarkably by a moderate V2<V1{V}_{2}<{V}_{1}V2​<V1​ via calculating the spectrum and charge excitation gaps, which highlights the experimentally feasible scheme of realizing the interaction driven topological phase by spatially decaying interactions on topologically trivial lattice models.
Electronic systems with quadratic band touchings, commonly found in two- and three-dimensional materials such as Bernal-stacked bilayer graphene, kagome metals, HgTe, and pyrochlore iridates, have attracted significant interest concerning the role of interactions in shaping their electronic properties. However, even in the simplest model of spinless fermions on a two-dimensional checkerboard lattice, the quantum phase diagram as a function of nearest-neighbor interaction remains under debate. We employ constrained-path quantum Monte Carlo simulations (CP-QMC) simulations to investigate the problem using a two-dimensional torus geometry. We cross-validate our results on small lattices by comparing them with density-matrix renormalization group calculations, finding quantitative agreement. In particular, we implement an improved optimization scheme within the CP-QMC simulations, enabling the identification of a bond-nematic Dirac semimetal phase that was found in tensor-network studies on cylindrical geometries, but remains inaccessible to Hartree-Fock mean-field methods. The CP-QMC approach makes it possible to establish the emergence of this phase in a geometry that preserves lattice rotational symmetry and permits extrapolation to the thermodynamic limit. Our results show that the quantum phase diagram of spinless fermions on the checkerboard lattice with nearest-neighbor repulsion features three interaction-induced phases at half filling: a quantum anomalous Hall insulator at weak coupling, a bond-nematic Dirac semimetal at intermediate coupling, and a site-nematic insulator at strong coupling.
We study an interacting spinless quadratic band touching model that realizes a topological Mott insulating state. We quench the interaction from a value corresponding to the nematic insulator to that of the quantum anomalous Hall (QAH) ordered phase. We perform time-dependent Hartree-Fock simulations and show that after the quench the system realizes an excited Dirac semimetal state, which is, however, unstable and spontaneously evolves to a state with inhomogeneous nematic and QAH order parameters. The modulations form a stripe pattern that grows exponentially with time until the local Chern marker reaches unity. The alternating QAH order defines a domain structure with boundaries that host chiral sublattice currents.
We study an interacting spinless quadratic band touching model that realizes a topological Mott insulating state. We quench the interaction from a value corresponding to the nematic insulator to that of the quantum anomalous Hall (QAH) ordered phase. We perform time-dependent Hartree-Fock simulations and show that after the quench the system realizes an excited Dirac semimetal state, which is however unstable and spontaneously evolves to a state with inhomogeneous nematic and QAH order parameters. The modulations form a stripe pattern that grows exponentially with time until the local Chern marker reaches unity. The alternating QAH order defines a domain structure with boundaries that host chiral sublattice currents.