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arXiv:1112.5124 · Physical Review B

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

Rong-Qiang He, Zhong-Yi Lu

Published Jul 6, 2012• 27 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.86.045105

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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.
The question of the existence of a spin liquid state in the half-filled Hubbard model on the honeycomb (also known as graphene) lattice is revisited. The variational cluster approximation, the cluster dynamical mean field theory, and the cluster dynamical impurity approximation are applied to various cluster systems. Assuming that the spin liquid phase coincides with the Mott insulating phase in this nonfrustrated system, we find that the Mott transition is preempted by a magnetic transition occurring at a lower value of the interaction U, and therefore the spin liquid phase does not occur. This conclusion is obtained using clusters with two bath orbitals connected to each boundary cluster site. We argue that using a single bath orbital per boundary site is insufficient and leads to the erroneous conclusion that the system is gapped for all nonzero values of U.
The periodized cluster dynamical mean-field theory (PCDMFT) combined with exact diagonalization as the impurity solver has been applied to the half-filled standard Hubbard model on the honeycomb lattice. A correlated Dirac semimetal is found for weak interactions and it transforms into an antiferromagnetic insulating phase for strong interactions via a first-order quantum phase transition, not intervened by a spin liquid phase in between. In this application, the PCDMFT introduces the partial translation symmetry, but cures well the problem caused by the translation symmetry breaking in the cluster dynamical mean-field theory studies for the same model, which gives rise to a spurious insulating phase in the weakly interacting region.
A spin liquid is a novel quantum state of matter with no conventional order parameter where a finite charge gap exists even though the band theory would predict metallic behavior. Finding a stable spin liquid in two or higher spatial dimensions is one of the most challenging and debated issues in condensed matter physics. Very recently, it has been reported that a model of graphene, i.e., the Hubbard model on the honeycomb lattice, can show a spin liquid ground state in a wide region of the phase diagram, between a semi-metal (SM) and an antiferromagnetic insulator (AFMI). Here, by performing numerically exact quantum Monte Carlo simulations, we extend the previous study to much larger clusters (containing up to 2592 sites), and find, if any, a very weak evidence of this spin liquid region. Instead, our calculations strongly indicate a direct and continuous quantum phase transition between SM and AFMI.
The effect of Coulomb correlations in the half-filled Hubbard model of the honeycomb lattice is studied within the dynamical cluster approximation (DCA) combined with exact diagonalization (ED) and continuous-time quantum Monte Carlo (QMC), for unit cells consisting of six-site rings. The important difference between this approach and the previously employed cluster dynamical mean-field theory (CDMFT) is that DCA preserves the translation symmetry of the system, while CDMFT violates this symmetry. As the Dirac cones of the honeycomb lattice are the consequence of perfect long-range order, DCA yields semimetallic behavior at small on-site Coulomb interactions UUU, whereas CDMFT gives rise to a spurious excitation gap even for very small UUU. This basic difference between the two cluster approaches is found regardless of whether ED or QMC is used as the impurity solver. At larger values of UUU, the lack of translation symmetry becomes less important, so that the CDMFT reveals a Mott gap, in qualitative agreement with large-scale QMC calculations. In contrast, the semimetallic phase obtained in DCA persists even at UUU values where CDMFT and large-scale QMC consistently show Mott-insulating behavior.
Many-body problem on the honeycomb lattice systems have been the subject of considerable experimental and theoretical interest. Here we investigate the phase transitions of the ionic Hubbard model on the honeycomb lattice with an alternate ionic potential for the half filling and hole doping cases by means of cellular dynamical mean field theory combining with continue time quantum Monte Carlo as an impurity solver. At half filling, as the increase of the interaction at a fixed ionic potential, we find the single particle gap decreases firstly, reaches a minimum at a critical interaction Uc, then increases upturn. At Uc, there is a band insulator to Mott insulator transition accompanying with the presence of the antiferromagnetic order. Away from half filing, the system shows three phases for the different values of hole density and interaction, paramagnetic metal, antiferromagnetic metal and ferromagnetic metal. Further, we present the staggered particle number, the double occupancy, the staggered magnetization, the uniform magnetization and the single particle spectral properties, which exhibit characteristic features for those phases.
Recent numerical work [Z. Y. Meng et al., Nature (London) 464, 847 (2010)] indicates the existence of a spin liquid (SL) phase that intervenes between the antiferromagnetic and semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To better understand the nature of this exotic phase, we study the quantum J(1)-J(2) spin model on the honeycomb lattice, which provides an effective description of the Mott insulating region of the Hubbard model. Employing the variational Monte Carlo approach, we analyze the phase diagram of the model. We find three phases-antiferromagnetic, an unusual Z(2) SL state, and a dimerized state with spontaneously broken rotational symmetry. We identify the Z(2) SL state as the likely candidate for the SL phase of the Hubbard model.