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arXiv:1710.08199 · Physical review. B./Physical review. B

Multiband dual fermion approach to quantum criticality in the Hubbard honeycomb lattice

Daniel Hirschmeier, Hartmut Hafermann, Alexander I. Lichtenstein

Published Mar 26, 2018• 24 citations
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Abstract

We study the Hubbard model on the honeycomb lattice in the vicinity of the quantum critical point by means of a multiband formulation of the dual fermion approach. Beyond the strong local correlations of the dynamical mean field, critical fluctuations on all length scales are included by means of a ladder diagram summation. Analysis of the susceptibility yields an estimate of the critical interaction strength of the quantum phase transition from a paramagnetic semimetal to an antiferromagnetic insulator, in good agreement to other numerical methods. We further estimate the crossover temperature to the renormalized classical regime. Our data imply that, at large interaction strengths, the Hubbard model on the honeycomb lattice behaves like a quantum nonlinear $\ensuremath{\sigma}$ model, while displaying signs of non-Fermi-liquid behavior.

DOI
10.1103/physrevb.97.115150

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We study the Hubbard model on the honeycomb lattice in the vicinity of the quantum critical point by means of a multiband formulation of the dual fermion approach. Beyond the strong local correlations of the dynamical mean field, critical fluctuations on all length scales are included by means of a ladder diagram summation. Analysis of the susceptibility yields an estimate of the critical interaction strength of the quantum phase transition from a paramagnetic semimetal to an antiferromagnetic insulator, in good agreement to other numerical methods. We further estimate the crossover temperature to the renormalized classical regime. Our data imply that, at large interaction strengths, the Hubbard model on the honeycomb lattice behaves like a quantum nonlinear \ensuremathσ\ensuremath{\sigma}\ensuremathσ model, while displaying signs of non-Fermi-liquid behavior.
Quantum phase transitions in the Hubbard model on the honeycomb lattice are investigated in the variational cluster approximation. The critical interaction for the paramagnetic to antiferromagnetic phase transition is found to be in remarkable agreement with a recent large-scale quantum Monte Carlo simulation. Calculated staggered magnetization increases continuously with UUU and thus we find the phase transition is of a second order. We also find that the semimetal-insulator transition occurs at infinitesimally small interaction and thus a paramagnetic insulating state appears in a wide interaction range. A crossover behavior of electrons from itinerant to localized character found in the calculated single-particle excitation spectra and short-range spin correlation functions indicates that an effective spin model for the paramagnetic insulating phase is far from a simple Heisenberg model with a nearest-neighbor exchange interaction.
The semimetal to antiferromagnet quantum phase transition of the Hubbard model on the honeycomb lattice has come to the forefront in the context of the proposal that a semimetal to spin liquid transition can occur before the transition to the antiferromagnetic phase. To study the semimetal to antiferromagnet transition, we generalize the two-particle self-consistent (TPSC) approach to the honeycomb lattice (a structure that can be realized in graphene for example). We show that the critical interaction strength where the transition occurs is ${U}_{c}/t=3.79\ifmmode\pm\else\textpm\fi{}0.01$, quite close to the value ${U}_{c}/t=3.869\ifmmode\pm\else\textpm\fi{}0.013$ reported using large-scale quantum Monte Carlo simulations. This reinforces the conclusion that the semimetal to spin-liquid transition is preempted by the transition to the antiferromagnet. Since TPSC satisfies the Mermin-Wagner theorem, we find temperature-dependent results for the antiferromagnetic and ferromagnetic correlation lengths as well as the dependence of double occupancy and of the renormalized spin and charge interactions on the bare interaction strength. We also estimate the value of the crossover temperature to the renormalized classical regime as a function of interaction strength.
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.
Fermionic quantum criticality in honeycomb and π\piπ-flux Hubbard models
We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the π\piπ-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.
We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the $\ensuremath{\pi}$-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.
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.