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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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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.

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  1. Department of Physics, Faculty of Science, Okayama University, Okayama, 700-8530, Japan

    Yoshihiro Nishiyama

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  1. Yoshihiro Nishiyama
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Correspondence to Yoshihiro Nishiyama.

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Nishiyama, Y. Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions. Eur. Phys. J. B 91, 280 (2018). https://doi.org/10.1140/epjb/e2018-90426-8

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  • DOI: https://doi.org/10.1140/epjb/e2018-90426-8

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