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:1506.00501 · Physical Review B

Topological phases of the Kitaev-Hubbard model at half filling

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

Published Mar 27, 2014• 15 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.89.115130

Related papers

Spin-Liquid Phase in the Hubbard Model on the Honeycomb Lattice.

Zi Yang Meng, Thomas C. Lang, Stefan Weßel +2 more

The Hubbard model encapsulates the physics of strongly correlated quantum systems in its most basic form. It has been studied intensively in the context of the high-temperature superconductivity. A number of novel phases were recently proposed for Hubbard-like models on the honeycomb lattice, the structure of graphene. We analyzed the Hubbard model of spin- \(\frac{1}{2}\) fermions on the honeycomb lattice at half-filling using large-scale quantum Monte Carlo simulations. We find that the weak coupling semimetal and the antiferromagnetic Mott insulator at strong interaction are separated by an extended gapped phase in an intermediate coupling regime. Exploring excitation gaps, various correlation functions as well as probing for flux quantization, we conclude that a quantum spin liquid, lacking any conventional order, emerges with local charge and spin correlations, best described by a resonating valence bonds state.

IEEE International Conference on High Performance Computing, Data, and Analytics•Jan 1, 2010•0 citations

Quarter-filled Kitaev-Hubbard model: A quantum Hall state in an optical lattice

Syed R. Hassan, Sandeep K. Goyal, R. Shankar +1 more

We analyze the physics of cold atoms in honeycomb optical lattices with on-site repulsion and spin-dependent hopping that breaks time-reversal symmetry. Such systems, at half filling and large on-site repulsion, have been proposed as a possible realization of the Kitaev model. The spin-dependent hopping breaks the spin degeneracy and, if strong enough, leads to four nonoverlapping bands in the noninteracting limit. These bands carry nonzero Chern number and therefore the noninteracting system has nonzero angular momentum and chiral edge states at 1/4 and 3/4 filling. We have investigated the effect of interactions on a quarter-filled system using the variational cluster perturbation theory and found that the critical spin-dependent hopping that separates the metal from the quantum Hall state is affected by interactions.

arXiv:1201.5874•Physical Review B•Jul 2, 2013•10 citations

Metal–Insulator Transition of Dirac Fermions: Variational Cluster Study

Masaki Ebato, Tatsuya Kaneko, Y. Ohta

A comparative study is made on the metal-insulator transition of Dirac fermions in the honeycomb and π-flux Hubbard models at half filling by means of the variational cluster approximation and cluster dynamical impurity approximation. Paying particular attention to the choice of the geometry of solver clusters and the inclusion of particle-bath sites, we show that the direct transition from the Dirac semimetallic state to the antiferromagnetic Mott insulator state occurs in these models, and therefore, the spin liquid phase is absent in the intermediate region, in agreement with recent quantum-Monte-Carlo--based calculations.

arXiv:1502.04435•Journal of the Physical Society of Japan•Mar 23, 2015•5 citations

Distinct-symmetry spin-liquid states and phase diagram of the Kitaev-Hubbard model

Long Liang, Ziqiang Wang, Yue Yu

We report the finding of a series of distinct-symmetry spin-liquid (SL) states and a rich phase diagram in a half-filled honeycomb lattice Hubbard model with spin-dependent hopping amplitude ${t}^{\ensuremath{'}}$. We first study the magnetic instability of the system and find two antiferromagnetic orders beyond a critical Hubbard $U$ which increases with the ratio ${t}^{\ensuremath{'}}/t$. For ${t}^{\ensuremath{'}}$ approaching $t$, the semimetal transforms to a $U(1)$ SL and then to the Kitaev ${Z}_{2}$ SL as $U$ increases. In a wide middle range of ${t}^{\ensuremath{'}}/t$, the latter is replaced by a $U(1)$ SL to $SU(2)$ SL transition. The physical properties of the stable SL phases are discussed.

arXiv:1311.3430•Physical Review B•Aug 11, 2014•6 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

Quantum cluster approach to the spinful Haldane-Hubbard model

Jingxiang Wu, Jean Paul Latyr Faye, David Sénéchal +1 more

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.

arXiv:1512.04498•Physical review. B./Physical review. B•Feb 17, 2016•34 citations
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′{t}^{\ensuremath{'}}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′)(U,{t}^{\ensuremath{'}})(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.
The Hubbard model encapsulates the physics of strongly correlated quantum systems in its most basic form. It has been studied intensively in the context of the high-temperature superconductivity. A number of novel phases were recently proposed for Hubbard-like models on the honeycomb lattice, the structure of graphene. We analyzed the Hubbard model of spin- 12\frac{1}{2}21​ fermions on the honeycomb lattice at half-filling using large-scale quantum Monte Carlo simulations. We find that the weak coupling semimetal and the antiferromagnetic Mott insulator at strong interaction are separated by an extended gapped phase in an intermediate coupling regime. Exploring excitation gaps, various correlation functions as well as probing for flux quantization, we conclude that a quantum spin liquid, lacking any conventional order, emerges with local charge and spin correlations, best described by a resonating valence bonds state.
We analyze the physics of cold atoms in honeycomb optical lattices with on-site repulsion and spin-dependent hopping that breaks time-reversal symmetry. Such systems, at half filling and large on-site repulsion, have been proposed as a possible realization of the Kitaev model. The spin-dependent hopping breaks the spin degeneracy and, if strong enough, leads to four nonoverlapping bands in the noninteracting limit. These bands carry nonzero Chern number and therefore the noninteracting system has nonzero angular momentum and chiral edge states at 1/4 and 3/4 filling. We have investigated the effect of interactions on a quarter-filled system using the variational cluster perturbation theory and found that the critical spin-dependent hopping that separates the metal from the quantum Hall state is affected by interactions.
A comparative study is made on the metal-insulator transition of Dirac fermions in the honeycomb and π-flux Hubbard models at half filling by means of the variational cluster approximation and cluster dynamical impurity approximation. Paying particular attention to the choice of the geometry of solver clusters and the inclusion of particle-bath sites, we show that the direct transition from the Dirac semimetallic state to the antiferromagnetic Mott insulator state occurs in these models, and therefore, the spin liquid phase is absent in the intermediate region, in agreement with recent quantum-Monte-Carlo--based calculations.
We report the finding of a series of distinct-symmetry spin-liquid (SL) states and a rich phase diagram in a half-filled honeycomb lattice Hubbard model with spin-dependent hopping amplitude ${t}^{\ensuremath{'}}$. We first study the magnetic instability of the system and find two antiferromagnetic orders beyond a critical Hubbard UUU which increases with the ratio ${t}^{\ensuremath{'}}/t$. For ${t}^{\ensuremath{'}}$ approaching ttt, the semimetal transforms to a U(1)U(1)U(1) SL and then to the Kitaev Z2{Z}_{2}Z2​ SL as UUU increases. In a wide middle range of ${t}^{\ensuremath{'}}/t$, the latter is replaced by a U(1)U(1)U(1) SL to SU(2)SU(2)SU(2) SL transition. The physical properties of the stable SL phases are discussed.
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.
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.