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Strongly repulsive anyons in one dimension

Florian Lange, Satoshi Ejima, and Holger Fehske
Phys. Rev. A 95, 063621 – Published 23 June 2017
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  • INTRODUCTION
  • ANYONIC HUBBARD MODEL
  • STRONG-COUPLING EXPANSIONS
  • SUMMARY AND OUTLOOK
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    To explore the static properties of the one-dimensional anyon-Hubbard model for a mean density of one particle per site, we apply perturbation theory with respect to the ratio between kinetic energy and interaction energy in the Mott insulating phase. The strong-coupling results for the ground-state energy, the single-particle excitation energies, and the momentum distribution functions up to 6th order in hopping are benchmarked against the numerically exact (infinite) density-matrix renormalization group technique. Since these analytic expressions are valid for any fractional phase θ of anyons, they will be of great value for a sufficiently reliable analysis of future experiments, avoiding extensive and costly numerical simulations.

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    • Received 24 April 2017

    DOI:https://doi.org/10.1103/PhysRevA.95.063621

    ©2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    AnyonsPhase diagramsQuantum phase transitionsSuperfluidity
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Florian Lange, Satoshi Ejima, and Holger Fehske

    • Institut für Physik, Ernst-Moritz–Arndt Universität Greifswald, D-17489 Greifswald, Germany

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    Vol. 95, Iss. 6 — June 2017

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    Images

    • Figure 1
      Figure 1

      Ground-state energy E0/4LU as a function of interaction strength t/U. nth-order strong-coupling results E0[n] of Eq. (16) are compared with the quasiexact iDMRG data E0ex for χ=100 (solid lines). The relative errors δrel=|(E0ex−E0[n])/E0ex| are given in semilogarithmic representation corresponding to the right y axis.

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    • Figure 2
      Figure 2

      Sixth-order strong-coupling expansions (dashed lines) of the single-hole and single-particle excitation energies, Eqs. (21) and (22), compared with numerical data by iMPS with the variational ansatz (solid lines).

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    • Figure 3
      Figure 3

      Excitation energies for one additional particle, the parameters being the same as in Fig. 2. The disagreement between perturbation theory and variational iMPS ansatz can be explained by the onset of the multiparticle continuum.

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    • Figure 4
      Figure 4

      Phase diagram of the one-dimensional anyon-Hubbard model (np≤5) for the fractional angle θ=π/4 [panel (a)], π/2 [panel (b)], and π [panel (c)] with Mott insulator (MI) and superfluid (SF) regions. The MI-SF boundaries (black lines) were determined by DMRG with system sizes up to L=128, open boundary conditions, and np≤5. The strong-coupling expansions up to 6th order in x show reasonable agreements with the numerical data.

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    • Figure 5
      Figure 5

      Momentum distribution function nb(k) (upper panels) and na(k) (lower panels) within the first Mott for various θ from DMRG with L=48 and PBCs (symbols) compared with 4th-order strong-coupling expansions (solid lines).

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    • Figure 6
      Figure 6

      Ground-state phase diagram of the Bose-Hubbard model (θ=0). The strong-coupling results (A1) and (A2) show a reasonable agreement with the DMRG data (black solid line).

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    • Figure 7
      Figure 7

      (a) Zoomed view of Fig. 4 showing the artificial upturn of the 6th-order perturbation result μ− at θ=π/4. (b) Single-hole excitation energy Eh(k) in the momentum space for θ=π/4 and t/U=0.25 by the 6th-order strong-coupling expansion (dashed line) compared with the iMPS results (circles). Star and cross symbols denote the correct and wrong minima to estimate chemical potential μ−, see text.

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    • Figure 8
      Figure 8

      Strong-coupling results of the boson (upper panel) and anyon (lower panel) correlation functions Cb/a(r) (closed symbols) for the distance r=1 to 4, compared with the iDMRG data for χ=100 (open symbols).

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