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arXiv:1504.06373 · Physical Review B

Antiferromagnetism in the Hubbard model on the honeycomb lattice: A two-particle self-consistent study

S. Arya, P. V. Sriluckshmy, Syed R. Hassan, A.–M. S. Tremblay

Published Jul 9, 2015• 46 citations
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Abstract

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.

DOI
10.1103/physrevb.92.045111

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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 Uc/t=3.79\ifmmode±\else\textpm\fi0.01{U}_{c}/t=3.79\ifmmode\pm\else\textpm\fi{}0.01Uc​/t=3.79\ifmmode±\else\textpm\fi0.01, quite close to the value Uc/t=3.869\ifmmode±\else\textpm\fi0.013{U}_{c}/t=3.869\ifmmode\pm\else\textpm\fi{}0.013Uc​/t=3.869\ifmmode±\else\textpm\fi0.013 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.
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.
Motivated by the fascinating magnetic properties in the half-filled Hubbard model on a honeycomb lattice, we calculate the spin susceptibility and estimate the magnetic transition by applying the two-particle self-consistent (TPSC) method. The diagonalized spin-susceptibility matrix has its maximum at Q = 0 , which indicates that an uniform magnetic order develops between the unit cells. The sign of the spin susceptibility between same sublattices is opposite to that between different sublattices. Therefore, an antiferromagnetic state develops in this system. We calculate the temperature dependence of the Stoner factor and estimate the critical temperature extrapolation. By applying the same analysis to several values of on-site interactions, we present the phase diagram of the magnetic state in the half-filled Hubbard model on a honeycomb lattice. Based on the phase diagram, the critical on-site interaction U c /t above which magnetism occurs at the ground state can be estimated as being approximately 3.81.
The Hubbard model on the honeycomb lattice undergoes a quantum phase transition from a semimetallic to a Mott insulating phase and from a disordered to an anti-ferromagnetically phase. We show that these transitions occur simultaneously and we calculate the critical coupling Uc=3.835(14)U_c=3.835(14)Uc​=3.835(14) as well as the critical exponents ν=1.181(43)\nu=1.181(43)ν=1.181(43) and β=0.898(37)\beta= 0.898(37)β=0.898(37) which are expected to fall into the SU(2)SU(2)SU(2) Gross-Neveu universality class. For this we employ Hybrid Monte Carlo simulations, extrapolate the single particle gap and the spin structure factors to the thermodynamic and continuous time limits, and perform a data collapse fit. We also determine the zero temperature values of single particle gap and staggered magnetisation on both sides of the phase transition.
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.
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.
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.