TY - JOUR
T1 - Magnon-bound-state hierarchy for the two-dimensional transverse-field Ising model in the ordered phase
AU - Nishiyama, Yoshihiro
N1 - Funding Information:
This work was supported by a Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science (Grant No. 25400402 ).
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, m23<…. Each ratio m2,3,…/m1 (m1: 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 m2,3,4, and the spectrum is analyzed with the finite-size-scaling method to estimate the universal mass-gap ratios.
AB - In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, m23<…. Each ratio m2,3,…/m1 (m1: 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 m2,3,4, and the spectrum is analyzed with the finite-size-scaling method to estimate the universal mass-gap ratios.
KW - Exact diagonalization method
KW - Magnon mass gaps
KW - Two-dimensional transverse-field Ising model
KW - Universal amplitude ratio
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U2 - 10.1016/j.physa.2016.07.045
DO - 10.1016/j.physa.2016.07.045
M3 - Article
AN - SCOPUS:84982671700
VL - 463
SP - 303
EP - 309
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
ER -