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

TL;DR

This study investigates the hierarchy of magnon bound states in the ordered phase of the two-dimensional transverse-field Ising model, revealing universal mass-gap ratios using exact diagonalization and finite-size scaling.

Contribution

It extends the understanding of magnon bound states and universal ratios to the 2+1 dimensional Ising model, which was previously less clear.

Findings

Identification of multiple magnon bound states

Estimation of universal mass-gap ratios

Application of exact diagonalization and finite-size scaling

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.