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arXiv:1005.2043 · Physical Review B

Interacting Dirac fermions on honeycomb lattice

Wéi Wú, Yao‐Hua Chen, Hong-Shuai Tao, Ning-Hua Tong, Wu-Ming Liu

Published Dec 2, 2010• 84 citations
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Abstract

We investigate the interacting Dirac fermions on honeycomb lattice by cluster dynamical mean-field theory (DMFT) combined with continuous-time quantum Monte Carlo simulation. A novel scenario for the semimetal-Mott insulator transition of the interacting Dirac fermions is found beyond the previous DMFT studies. Our results suggest that for weak interaction, the system is semimetal and the Fermi velocity keeps constant. The system undergoes a second-order Mott transition with increasing the interaction strength. We demonstrate that the nonlocal spatial correlations play a vital role in the Mott transition on the honeycomb lattice. A phase diagram of Mott transition is presented. We also elaborate the experimental protocol to observe this phase transition by the ultracold atoms on optical honeycomb lattice.

DOI
10.1103/physrevb.82.245102

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•Aug 17, 2021•1 citation
We investigate the interacting Dirac fermions on honeycomb lattice by cluster dynamical mean-field theory (DMFT) combined with continuous-time quantum Monte Carlo simulation. A novel scenario for the semimetal-Mott insulator transition of the interacting Dirac fermions is found beyond the previous DMFT studies. Our results suggest that for weak interaction, the system is semimetal and the Fermi velocity keeps constant. The system undergoes a second-order Mott transition with increasing the interaction strength. We demonstrate that the nonlocal spatial correlations play a vital role in the Mott transition on the honeycomb lattice. A phase diagram of Mott transition is presented. We also elaborate the experimental protocol to observe this phase transition by the ultracold atoms on optical honeycomb lattice.
The role of nonlocal Coulomb correlations in the honeycomb lattice is investigated within cluster dynamical mean field theory combined with finite-temperature exact diagonalization. The paramagnetic semimetal-to-insulator transition is found to be in excellent agreement with finite-size determinantal quantum Monte Carlo simulations and with cluster dynamical mean field calculations based on the continuous-time quantum Monte Carlo approach. As expected, the critical Coulomb energy is much lower than within a local or single-site formulation. Short-range correlations are shown to give rise to a pseudogap and concomitant non-Fermi-liquid behavior within a narrow range below the Mott transition.
We investigate two-component ultracold fermions loaded in a decorated honeycomb lattice described by the Hubbard model with repulsive interactions and nearest-neighbor hopping. The phase transitions are studied by combining the cellular dynamical mean-field theory with the continuous-time quantum Monte Carlo method. For weak interactions, the quadratic band crossing point is broken to a linear band crossing point and the system becomes a semimetal. With increasing interaction, the system undergoes a first-order phase transition to an antiferromagnetic Mott insulator at low temperatures. Below the critical temperature, due to the charge nematic fluctuation, a nematic metal forms between the semimetal and the antiferromagnetic Mott insulator. The effects of lattice anisotropy are also addressed. Furthermore, we discuss how to detect these phases in real experiments.
We study the one-band Hubbard model on the honeycomb lattice using a combination of quantum Monte Carlo (QMC) simulations and static as well as dynamical mean-field theory (DMFT). This model is known to show a quantum phase transition between a Dirac semimetal and the antiferromagnetic insulator. The aim of this paper is to provide a detailed comparison between these approaches by computing static properties, notably ground-state energy, single-particle gap, double occupancy, and staggered magnetization, as well as dynamical quantities such as the single-particle spectral function. At the static mean-field level, local moments cannot be generated without breaking the SU(2) spin symmetry. The DMFT approximation accounts for temporal fluctuations and thus captures both the evolution of the double occupancy and the resulting local moment formation in the paramagnetic phase. As a consequence, the DMFT approximation is found to be very accurate in the Dirac semimetallic phase where local moment formation is present and the spin correlation length small. However, in the vicinity of the fermion quantum critical point, the spin correlation length diverges and the spontaneous SU(2) symmetry breaking leads to low-lying Goldstone modes in the magnetically ordered phase. The impact of these spin fluctuations on the single-particle spectral function---waterfall features and narrow spin-polaron bands---is only visible in the lattice QMC approach.
Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)×U(1) symmetry. Using large-scale auxiliary-field quantum Monte Carlo (QMC) simulations, we locate two zero-temperature phase transitions as function of increasing interaction strength. First, we observe a continuous transition from the weakly interacting semimetal to a different semimetallic phase in which the SO(3) symmetry is spontaneously broken and where two out of three Dirac cones acquire a mass gap. The associated quantum critical point can be understood in terms of a Gross-Neveu-SO(3) theory. Second, we subsequently observe a transition toward an insulating phase in which the SO(3) symmetry is restored and the U(1) symmetry is spontaneously broken. While strongly first order at the mean-field level, the QMC data are consistent with a direct and continuous transition. It is thus a candidate for a new type of deconfined quantum critical point that features gapless fermionic degrees of freedom.
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.
Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)×\times×U(1) symmetry. Using large-scale auxiliary- field quantum Monte Carlo (QMC) simulations, we locate two zero-temperature phase transitions as function of increasing interaction strength. First, we observe a continuous transition from the weakly-interacting semimetal to a different semimetallic phase in which the SO(3) symmetry is spontaneously broken and where two out of three Dirac cones acquire a mass gap. The associated quantum critical point can be understood in terms of a Gross-Neveu-SO(3) theory. Second, we subsequently observe a transition towards an insulating phase in which the SO(3) symmetry is restored and the U(1) symmetry is spontaneously broken. While strongly first order at the mean-field level, the QMC data is consistent with a direct and continuous transition. It is thus a candidate for a new type of deconfined quantum critical point that features gapless fermionic degrees of freedom.