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Mott transition and magnetism of the triangular-lattice Hubbard model with next-nearest-neighbor hopping

Kazuma Misumi, Tatsuya Kaneko, and Yukinori Ohta
Phys. Rev. B 95, 075124 – Published 13 February 2017
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  • INTRODUCTION
  • MODEL AND METHOD
  • RESULTS OF CALCULATION
  • SUMMARY
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    The variational cluster approximation is used to study the isotropic triangular-lattice Hubbard model at half filling, taking into account the nearest-neighbor (t1) and next-nearest-neighbor (t2) hopping parameters for magnetic frustrations. We determine the ground-state phase diagram of the model. In the strong-correlation regime, the 120∘ Néel- and stripe-ordered phases appear, and a nonmagnetic insulating phase emerges in between. In the intermediate correlation regime, the nonmagnetic insulating phase expands to a wider parameter region, which goes into a paramagnetic metallic phase in the weak-correlation regime. The critical phase boundary of the Mott metal-insulator transition is discussed in terms of the van Hove singularity evident in the calculated density of states and single-particle spectral function.

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    • Received 5 May 2016
    • Revised 12 January 2017

    DOI:https://doi.org/10.1103/PhysRevB.95.075124

    ©2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Frustrated magnetismMagnetic texture
    1. Techniques
    Cluster methodsHeisenberg modelHubbard modelVariational approach
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Kazuma Misumi, Tatsuya Kaneko, and Yukinori Ohta

    • Department of Physics, Chiba University, Chiba 263-8522, Japan

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    Issue

    Vol. 95, Iss. 7 — 15 February 2017

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    Images

    • Figure 1
      Figure 1

      Schematic representations of (a) the triangular-lattice Hubbard model with the nearest-neighbor (t1) and next-nearest-neighbor (t2) hopping parameters, (b) the 120∘ Néel order, and (c) the stripe order. The arrows represent the directions of electron spins on the A, B, and C sublattices defined by different colors.

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    • Figure 2
      Figure 2

      (a) The reference system of the 12-site cluster used in our analysis; the three-sublattice system corresponding to the 120∘ Néel order (left) and the two-sublattice system corresponding to the stripe order (right). (b) The first Brillouin zone of our triangular-lattice Hubbard model: Γ(0,0),K(4π/3,0), and M(π,π/3).

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    • Figure 3
      Figure 3

      Calculated ground-state phase diagram of our model in the strong-correlation regime (U/t1=60). Top: the order parameters of the 120∘ Néel- and stripe-ordered phases. Solid (open) symbols indicate that the state is stable (metastable). Bottom: the ground-state energies (per site) of the ordered phases compared with that of the disordered phase. Inset: the enlargement of the energy difference ΔE between the 120∘ ordered and disordered phases.

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    • Figure 4
      Figure 4

      Calculated ground-state phase diagram of our model in the intermediate- to weak-correlation regime, which includes the 120∘ Néel-ordered, stripe-ordered, nonmagnetic insulating, and paramagnetic metallic phases. The circle and triangle at U/t1=60 indicate the calculated phase boundaries of the 120∘ Néel order and stripe order, respectively, shown in Fig. 3.

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    • Figure 5
      Figure 5

      Calculated charge gap Δ (top) and order parameters M120∘ and Mstr (bottom) of our model as a function of U/t1.

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    • Figure 6
      Figure 6

      Calculated DOS of our model in the metallic state (left) and insulating state without long-range magnetic orders (right). η/t1=0.1 is assumed. The vertical line in each panel indicates the Fermi level.

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    • Figure 7
      Figure 7

      Calculated single-particle spectral function A(k,ω) in the paramagnetic state of our model. The wave vector k is chosen along the line connecting Γ, K, and M points of the Brillouin zone [see Fig. 2]. η/t1=0.1 is assumed. The noninteracting band dispersion is also shown by a thin solid curve in each of the upper panels. The Fermi level (indicated by the vertical line) is set at ω/t1=0.

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    • Figure 8
      Figure 8

      Calculated generalized magnetic susceptibility in the noninteracting limit χ0(q) defined in Eq. (11). The corresponding Fermi surface is shown in each panel, where the first Brillouin zone is indicated by a hexagon.

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    • Figure 9
      Figure 9

      (a) Cluster-size and cluster-shape dependencies of the phase boundaries between the 120∘ Néel-ordered, stripe-ordered, nonmagnetic insulating, and paramagnetic metallic phases. Unlabeled lines are the results shown in Fig. 4. (b) Schematic representations of the clusters used in the calculations; in the six-site cluster calculation, we combine two of them to reproduce the 120∘ Néel order.

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