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arXiv · 1608.00083

Magnon-bound-state hierarchy for the two-dimensional transverse-field Ising model in the ordered phase

Yoshihiro Nishiyama
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Abstract

In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, $m_2<m_3 < \dots$. Each ratio $m_{2,3,\dots}/m_1$ ($m_1$: the single-magnon mass) is expected to be a universal constant in the vicinity of the critical point. In this paper, we devote ourselves to the $(2+1)$-dimensional counterpart, for which the universal hierarchical character remains unclear. We employed the exact diagonalization method, which enables us to calculate the dynamical susceptibility via the continued-fraction expansion. Thereby, we observe a variety of signals including $m_{2,3,4}$, and the spectrum is analyzed with the finite-size-scaling method to estimate the universal mass-gap ratios.

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Yoshihiro Nishiyama. 2016-07-30. Magnon-bound-state hierarchy for the two-dimensional transverse-field Ising model in the ordered phase. https://doi.org/10.1016/j.physa.2016.07.045

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