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

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.

References in corpus (3)

• "Quasi-particle breakdown" in the quasi-one-dimensional Ising ferromagnet CoNb${}_2$O${}_6$
• Bound-state energy of the d=3 Ising model in the broken-symmetry phase: Suppressed finite-size corrections
• Universal critical behavior of the two-magnon-bound-state mass gap for the (2+1)-dimensional Ising model

Cited by in corpus (2)

• Persistent oscillations after quantum quenches in $d$ dimensions
• Quantum quenches with long range interactions