https://doi.org/10.1140/epjb/e2018-90426-8
Regular Article
Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions
Department of Physics, Faculty of Science, Okayama University,
Okayama
700-8530, Japan
a e-mail: nisiyama@psun.phys.okayama-u.ac.jp
Received:
1
July
2018
Received in final form:
2
September
2018
Published online: 13 November 2018
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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2018