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Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions

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  • Yoshihiro Nishiyama

    (Faculty of Science, Okayama University)

Abstract

The quantum Ising chain with the interaction decaying as a power law 1∕r1+σ of the distance between spins r was investigated numerically. A particular attention was paid to the low-energy spectrum, namely, the single-magnon and two-magnon-bound-state masses, m1,2, respectively, in the ordered phase. It is anticipated that for each σ, the scaled bound-state mass m2∕m1 should take a universal constant (critical amplitude ratio) in the vicinity of the critical point. In this paper, we calculated the amplitude ratio m2∕m1 with the exact diagonalization method, which yields the spectral information, such as m1,2 directly. As a result, we found that the scaled mass m2∕m1 exhibits a non-monotonic dependence on σ; that is, the bound state is stabilized by an intermediate value of σ. Such a feature is accordant with a recent observation based on the non-perturbative-renormalization-group method.

Suggested Citation

  • Yoshihiro Nishiyama, 2018. "Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(11), pages 1-6, November.
    • Handle: RePEc:spr:eurphb:v:91:y:2018:i:11:d:10.1140_epjb_e2018-90426-8
    DOI: 10.1140/epjb/e2018-90426-8
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    Statistical and Nonlinear Physics;

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