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Dynamic response of spin-2 bosons in one-dimensional optical lattices

Florian Lange, Satoshi Ejima, and Holger Fehske
Phys. Rev. A 100, 023623 – Published 23 August 2019
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  • INTRODUCTION
  • MODEL AND METHOD
  • STATIC CORRELATIONS
  • DYNAMIC SPIN STRUCTURE FACTOR
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We investigate the spin-2 chain model corresponding to the small hopping limit of the spin-2 Bose-Hubbard model using density-matrix renormalization-group and time-evolution techniques. We calculate both static correlation functions and the dynamic structure factor. The dynamic structure factor in the dimerized phase differs significantly between parameters near the SU(5)-symmetric point and those deeper in the phase where the dimerization is strong. In the former case, most of the spectral weight is concentrated in a single excitation line, while in the latter case, a broad excitation continuum shows up. For the trimerized phase, we find gapless excitations at momenta k=±2π/3 in agreement with previous results, although the visibility of these excitations in the dynamic spin response depends strongly on the specific parameters. We also consider parameters for specific atoms which may be relevant for future optical-lattice experiments.

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    • Received 15 May 2019

    DOI:https://doi.org/10.1103/PhysRevA.100.023623

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Cold gases in optical lattices
    Atomic, Molecular & Optical

    Authors & Affiliations

    Florian Lange, Satoshi Ejima, and Holger Fehske

    • Institut für Physik, Universität Greifswald, 17489 Greifswald, Germany

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    Issue

    Vol. 100, Iss. 2 — August 2019

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    Images

    • Figure 1
      Figure 1

      Schematic phase diagram of the model (2) as a ternary plot of the variables (ε0,ε2,ε4)/(ε0+ε2+ε4) [15]. The circles labeled (a)–(f) indicate the model-parameter values used in the corresponding panels of Fig. 4.

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    • Figure 2
      Figure 2

      (a) Spin-spin and (b) quadrupolar correlation functions defined in Eqs. (4) and (5) for the dimerized phase. A bond dimension of χ=4000 was used in the IDMRG calculations. The insets display the same results using a semilogarithmic representation. (c) Dimerization order parameter OD [Eq. (3)] as a function of ε2/ε0.

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    • Figure 3
      Figure 3

      Spin-spin correlation function (4) in the trimerized phase. The inset uses a log-log scale for the same data.

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    • Figure 4
      Figure 4

      Dynamic structure factor S(k,ω) [Eq. (6)] in the (a)–(c) dimerized and (d)–(f) trimerized phases. The parameters used are indicated in the phase diagram of Fig. 1. In (c) the exact onset of the excitation continuum according to Eq. (8) is marked by the dashed line. The energy unit is |ε0| for the dimerized and |ε2| for the trimerized phase. All spectral functions are convolved with a Gaussian function with σ=0.075 using the same energy scale.

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    • Figure 5
      Figure 5

      Dynamic structure factor for parameters calculated using the scattering lengths of Ref. [37], namely, (ε0,ε2,ε4)/(ε0+ε2+ε4)≈(0.43,0.33,0.24) and (0.36,0.34,0.30) for Na23 and Rb87, respectively. Energy units and Gaussian broadening are as in Fig. 4.

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