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Analytical approach for the Mott transition in the Kane-Mele-Hubbard model

Joel Hutchinson, Philipp W. Klein, and Karyn Le Hur
Phys. Rev. B 104, 075120 – Published 13 August 2021
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  • INTRODUCTION
  • STOCHASTIC METHOD
  • RESULTS
  • FLUCTUATIONS
  • COMPARISON OF ENERGETICS
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • References

    Abstract

    The description of interactions in strongly correlated topological phases of matter remains a challenge. Here, we develop a stochastic functional approach for interacting topological insulators including both charge and spin channels. We find that the Mott transition of the Kane-Mele-Hubbard model may be described by the variational principle with one equation. We present different views of this equation from the electron Green's function, the free-energy, and the Hellmann-Feynman theorem. In particular, we show the stability of the transition line towards fluctuations, in good agreement with numerical results. The band gap remains finite at the transition and the Mott phase is characterized by antiferromagnetism in the x−y plane. The interacting topological phase is described through a Z2 number related to helical edge modes. Our results then show that improving stochastic approaches can give further insight on the understanding of interacting phases of matter.

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    • Received 27 May 2021
    • Revised 7 July 2021
    • Accepted 8 July 2021

    DOI:https://doi.org/10.1103/PhysRevB.104.075120

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    AntiferromagnetismChern insulatorsMagnetic phase transitionsMagnonsQuantum phase transitionsSecond order phase transitionsSymmetry protected topological statesTopological phase transition
    1. Physical Systems
    GrapheneHoneycomb latticeMott insulators
    1. Techniques
    Hubbard modelPath integralsVariational approach
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Joel Hutchinson, Philipp W. Klein, and Karyn Le Hur

    • CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91128 Palaiseau, France

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    Issue

    Vol. 104, Iss. 7 — 15 August 2021

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    Images

    • Figure 1
      Figure 1

      Magnetization profile for t2=0.3t1.

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    • Figure 2
      Figure 2

      Onset of antiferromagnetic XY order at the Mott transition versus t2/t1 from the variational stochastic approach defined through Uc in Eq. (22) (solid blue line). This is compared to previous data from CDMFT in orange (Ref. [10]) and QMC in green (Ref. [12]).

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    • Figure 3
      Figure 3

      Imaginary parts of the polarization functions for λ=0.1, mx=0.1, my=0 in the q̃−ω plane. (a) −ImΠ00(q,ω), showing the gap q̃2+4m̃2 and the optical absorption edge demarcating the white region from the red. (b) ImΠxx(q,ω).

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    • Figure 4
      Figure 4

      Collective spin-mode dispersions showing the out-of-plane and in-plane optical modes, and the acoustic Goldstone mode. The dashed black line shows the Landau damping edge above which the imaginary part of the polarization functions becomes nonzero. Here, the parameters are fixed deep in the Mott phase such that t2=0.2 and U=7 for which the mean-field value of the in-plane magnetization is (ϕx)2+(ϕy)2≈0.21.

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    • Figure 5
      Figure 5

      (a) Mean-field values of the ϕ components on sublattices A (left) and B (right) for t2=0.5t1. ϕx and ϕy components are degenerate, here we just show one possible orientation of the in-plane field. (b) Magnitude of the combined magnetic order parameter in the U−t2 plane.

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