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:1512.04498 · Physical review. B./Physical review. B

Quantum cluster approach to the spinful Haldane-Hubbard model

Jingxiang Wu, Jean Paul Latyr Faye, David Sénéchal, Joseph Maciejko

Published Feb 17, 2016• 34 citations
arXivHTMLPDF

Abstract

We study the spinful fermionic Haldane-Hubbard model at half-filling using a combination of quantum cluster methods: cluster perturbation theory, the variational cluster approximation, and cluster dynamical mean-field theory. We explore possible zero-temperature phases of the model as a function of onsite repulsive interaction strength and next-nearest-neighbor hopping amplitude and phase. Our approach allows us to access the regime of intermediate interaction strength, where charge fluctuations are significant and effective spin model descriptions may not be justified. Our approach also improves upon mean-field solutions of the Haldane-Hubbard model by retaining local quantum fluctuations and treating them nonperturbatively. We find a correlated topological Chern insulator for weak interactions and a topologically trivial N\'eel antiferromagnetic insulator for strong interactions. For intermediate interactions, we find that topologically nontrivial N\'eel antiferromagnetic insulating phases and/or a topologically nontrivial nonmagnetic insulating phase may be stabilized.

DOI
10.1103/physrevb.93.075131

Related papers

Charge ordering in extended Hubbard models: Variational cluster approach

Markus Aichhorn, Hans Gerd Evertz, Wolfgang von der Linden +1 more

We present a generalization of the recently proposed variational cluster perturbation theory to extended Hubbard models at half-filling with repulsive nearest neighbor interaction. The method takes into account short-range correlations correctly by the exact diagonalization of clusters of finite size, whereas long-range order beyond the size of the clusters is treated on a mean-field level. For one dimension, we show that quantum Monte Carlo and density-matrix renormalization-group results can be reproduced with very good accuracy. Moreover we apply the method to the two-dimensional extended Hubbard model on a square lattice. In contrast to the one-dimensional case, a first order phase transition between spin density wave phase and charge density wave phase is found as function of the nearest-neighbor interaction at onsite interactions $U\ensuremath{\geqslant}3t$. The single-particle spectral function is calculated for both the one-dimensional and the two-dimensional system.

arXiv:cond-mat/0402580•Physical Review B•Dec 3, 2004•99 citations

Topological Mott Insulators

S. Raghu, Xiao-Liang Qi, Carsten Honerkamp A +1 more

We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin fermion models, respectively. The mean-field phase diagram is presented and the fluctuations are treated within the random phase approximation. Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.

arXiv:0710.0030•Physical Review Letters•Apr 15, 2008•659 citations

Topological phases of the Kitaev-Hubbard model at half filling

Jean Paul Latyr Faye, David Sénéchal, Syed R. Hassan

The Kitaev-Hubbard model of interacting fermions is defined on the honeycomb lattice and, at strong coupling, interpolates between the Heisenberg model and the Kitaev model. It is basically a Hubbard model with ordinary hopping $t$ and spin-dependent hopping ${t}^{\ensuremath{'}}$. We study this model in the weak to intermediate coupling regime, at half filling, using the cellular dynamical impurity approximation (CDIA), an approach related to dynamical mean field theory but based on Potthoff's variational principle. We identify four phases in the $(U,{t}^{\ensuremath{'}})$ plane: two semimetallic phases with different numbers of Dirac points, an antiferromagnetic insulator, and an algebraic spin liquid. The last two are separated by a first-order transition. These four phases all meet at a single point and could be realized in cold atom systems.

arXiv:1506.00501•Physical Review B•Mar 27, 2014•15 citations

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

Slave spins away from half filling: Cluster mean-field theory of the Hubbard and extended Hubbard models

Syed R. Hassan, Luca de’ Medici

A slave-spin representation of fermion operators has recently been proposed for the half-filled single and multiband Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. We solve the resulting spin problem using the cluster mean-field approximation. This approximation takes short-range correlations into account by exact diagonalization on the cluster, whereas long-range correlations beyond the size of clusters are treated at the mean-field level. In the limit where the cluster has only one site and the interaction strength $U$ is infinite, this approach reduces to the Gutzwiller approximation. There are some qualitative differences when the size of the cluster is finite. We first compute the critical $U$ for the Mott transition as a function of a frustrating nearest-neighbor interaction on lattices relevant for various correlated systems, namely, the cobaltates, the layered organic superconductors and the high-temperature superconductors. For the triangular lattice, we also study the extended Hubbard model with nearest-neighbor repulsion. In addition to a uniform metallic state, we find a $\sqrt{(3)}\ifmmode\times\else\texttimes\fi{}\sqrt{(3)}$ charge density wave in a broad doping regime, including commensurate ones. We find that in the large $U$ limit, intersite Coulomb repulsion $V$ strongly suppresses the single-particle weight of the metallic state.

arXiv:0805.3550•Physical Review B•Jan 12, 2010•81 citations

Cluster dynamical mean field theory of quantum phases on a honeycomb lattice

Rong-Qiang He, Zhong-Yi Lu

We report the cluster dynamical mean field theory calculations performed for the ground state of the half filled Hubbard model on a honeycomb lattice with exact diagonalization on the cluster-impurity solver. Through using elaborate numerical analytic continuation, we identify the existence of a ``spin liquid'' from the on-site interaction $U=0$ to ${U}_{c}$ (between $4.6t$ and $4.85t$) with a smooth crossover correspondingly from the charge fluctuation dominating phase into the charge correlation dominating phase. The semimetallic state exits only at $U=0$. We further find that the magnetic phase transition at ${U}_{c}$ from the spin liquid to the N\'eel antiferromagnetic Mott insulating phase is a first-order quantum phase transition. We also show that the charge fluctuation plays a substantial role on keeping the spin liquid phase against the emergence of a magnetic order.

arXiv:1112.5124•Physical Review B•Jul 6, 2012•27 citations
We study the spinful fermionic Haldane-Hubbard model at half-filling using a combination of quantum cluster methods: cluster perturbation theory, the variational cluster approximation, and cluster dynamical mean-field theory. We explore possible zero-temperature phases of the model as a function of onsite repulsive interaction strength and next-nearest-neighbor hopping amplitude and phase. Our approach allows us to access the regime of intermediate interaction strength, where charge fluctuations are significant and effective spin model descriptions may not be justified. Our approach also improves upon mean-field solutions of the Haldane-Hubbard model by retaining local quantum fluctuations and treating them nonperturbatively. We find a correlated topological Chern insulator for weak interactions and a topologically trivial N'eel antiferromagnetic insulator for strong interactions. For intermediate interactions, we find that topologically nontrivial N'eel antiferromagnetic insulating phases and/or a topologically nontrivial nonmagnetic insulating phase may be stabilized.
We present a generalization of the recently proposed variational cluster perturbation theory to extended Hubbard models at half-filling with repulsive nearest neighbor interaction. The method takes into account short-range correlations correctly by the exact diagonalization of clusters of finite size, whereas long-range order beyond the size of the clusters is treated on a mean-field level. For one dimension, we show that quantum Monte Carlo and density-matrix renormalization-group results can be reproduced with very good accuracy. Moreover we apply the method to the two-dimensional extended Hubbard model on a square lattice. In contrast to the one-dimensional case, a first order phase transition between spin density wave phase and charge density wave phase is found as function of the nearest-neighbor interaction at onsite interactions $U\ensuremath{\geqslant}3t$. The single-particle spectral function is calculated for both the one-dimensional and the two-dimensional system.
We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin fermion models, respectively. The mean-field phase diagram is presented and the fluctuations are treated within the random phase approximation. Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.
The Kitaev-Hubbard model of interacting fermions is defined on the honeycomb lattice and, at strong coupling, interpolates between the Heisenberg model and the Kitaev model. It is basically a Hubbard model with ordinary hopping ttt and spin-dependent hopping ${t}^{\ensuremath{'}}$. We study this model in the weak to intermediate coupling regime, at half filling, using the cellular dynamical impurity approximation (CDIA), an approach related to dynamical mean field theory but based on Potthoff's variational principle. We identify four phases in the $(U,{t}^{\ensuremath{'}})$ plane: two semimetallic phases with different numbers of Dirac points, an antiferromagnetic insulator, and an algebraic spin liquid. The last two are separated by a first-order transition. These four phases all meet at a single point and could be realized in cold atom systems.
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.
A slave-spin representation of fermion operators has recently been proposed for the half-filled single and multiband Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. We solve the resulting spin problem using the cluster mean-field approximation. This approximation takes short-range correlations into account by exact diagonalization on the cluster, whereas long-range correlations beyond the size of clusters are treated at the mean-field level. In the limit where the cluster has only one site and the interaction strength UUU is infinite, this approach reduces to the Gutzwiller approximation. There are some qualitative differences when the size of the cluster is finite. We first compute the critical UUU for the Mott transition as a function of a frustrating nearest-neighbor interaction on lattices relevant for various correlated systems, namely, the cobaltates, the layered organic superconductors and the high-temperature superconductors. For the triangular lattice, we also study the extended Hubbard model with nearest-neighbor repulsion. In addition to a uniform metallic state, we find a $\sqrt{(3)}\ifmmode\times\else\texttimes\fi{}\sqrt{(3)}$ charge density wave in a broad doping regime, including commensurate ones. We find that in the large UUU limit, intersite Coulomb repulsion VVV strongly suppresses the single-particle weight of the metallic state.
We report the cluster dynamical mean field theory calculations performed for the ground state of the half filled Hubbard model on a honeycomb lattice with exact diagonalization on the cluster-impurity solver. Through using elaborate numerical analytic continuation, we identify the existence of a ``spin liquid'' from the on-site interaction U=0U=0U=0 to Uc{U}_{c}Uc​ (between 4.6t4.6t4.6t and 4.85t4.85t4.85t) with a smooth crossover correspondingly from the charge fluctuation dominating phase into the charge correlation dominating phase. The semimetallic state exits only at U=0U=0U=0. We further find that the magnetic phase transition at Uc{U}_{c}Uc​ from the spin liquid to the N\'eel antiferromagnetic Mott insulating phase is a first-order quantum phase transition. We also show that the charge fluctuation plays a substantial role on keeping the spin liquid phase against the emergence of a magnetic order.