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

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 m2m1 should take a universal constant (critical amplitude ratio) in the vicinity of the critical point. In this paper, we calculated the amplitude ratio m2m1 with the exact diagonalization method, which yields the spectral information, such as m1,2 directly. As a result, we found that the scaled mass m2m1 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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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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Keywords

  • Statistical and Nonlinear Physics