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Holon-doublon binding as the mechanism for the Mott transition

Peter Prelovšek, Jure Kokalj, Zala Lenarčič, and Ross H. McKenzie
Phys. Rev. B 92, 235155 – Published 31 December 2015
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  • INTRODUCTION
  • SINGLE HOLON-DOUBLON PAIR BINDING
  • HOLON-DOUBLON PAIR IN A GENERAL SPIN…
  • FINITE HOLON-DOUBLON PAIR DENSITY
  • CONCLUSIONS AND IMPLICATIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We study the binding of a holon to a doublon in a half-filled Hubbard model as the mechanism of the zero-temperature metal-insulator transition. In a spin polarized system a single holon-doublon (HD) pair exhibits a binding transition on a 3D lattice, or a sharp crossover on a 2D lattice, corresponding well to the standard Mott transition in unpolarized systems. We extend the HD-pair study towards nonpolarized systems by considering more general spin background and by treating the finite HD density within a BCS-type approximation. Both approaches lead to a discontinuous transition away from the fully polarized system and give density correlations consistent with numerical results on a triangular lattice.

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    • Received 19 May 2015
    • Revised 11 December 2015

    DOI:https://doi.org/10.1103/PhysRevB.92.235155

    ©2015 American Physical Society

    Authors & Affiliations

    Peter Prelovšek1,2, Jure Kokalj1, Zala Lenarčič1, and Ross H. McKenzie3

    • 1J. Stefan Institute, SI-1000 Ljubljana, Slovenia
    • 2Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
    • 3School of Mathematics and Physics, University of Queensland, Brisbane, 4072 Queensland, Australia

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    Issue

    Vol. 92, Iss. 23 — 15 December 2015

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    Images

    • Figure 1
      Figure 1

      Phase diagram of the Hubbard model on a triangular lattice at half-filling as calculated from the BCS-type approximation and exact diagonalization (Lanczos) results. The Lanczos results are for magnetization m≠0 calculated at Nd holon-doublon pairs and system sizes N with values Nd/N=2/100,2/36, and 3/36, while result for m=0 is from Ref. [8]. Right panels show a schematic unbound (bound) holon-doublon pair in the metallic (insulating) phase on a triangular lattice with a nonzero spin polarization.

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    • Figure 2
      Figure 2

      Charge gap Δc vs U for the Hubbard model on triangular lattice. The results shown are calculated for a single holon-doublon (HD) pair at m∼1/2 (thick blue line), a single HD pair in an unpolarized spin background m=0 within the retraceable-path approximation (thin black line), and numerically for m=0 (red line with points).

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    • Figure 3
      Figure 3

      Double occupancy D (per double number of pairs 2Nd) vs U. The results shown are calculated for m∼1/2 with a single HD pair (denoted 1HD), for a single HD pair within the RPa (denoted RP approx.), with FTLM and taken from Ref. [8] (denoted FTLM), with exact diagonalization at T=0 and various m (denoted ED), and with BCS approximation for particular m (denoted BCS).

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    • Figure 4
      Figure 4

      Doublon-holon Cdh and doublon-doublon Cdd correlations vs distance r for different U/t evaluated for two HD pairs, Nd=2, on N=64 sites. Results obtained by using the full ED (lines) can be compared to the ones evaluated within the BCS wave function for U/t=6,8 (points).

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