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

Yoshihiro Nishiyama

doi:10.1016/j.physa.2016.07.045

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

Yoshihiro Nishiyama

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, m₂<m₃<…. Each ratio m_2,3,…/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 m_2,3,4, and the spectrum is analyzed with the finite-size-scaling method to estimate the universal mass-gap ratios.

Original language	English
Pages (from-to)	303-309
Number of pages	7
Journal	Physica A: Statistical Mechanics and its Applications
Volume	463
DOIs	https://doi.org/10.1016/j.physa.2016.07.045
Publication status	Published - Dec 1 2016

Keywords

Exact diagonalization method
Magnon mass gaps
Two-dimensional transverse-field Ising model
Universal amplitude ratio

ASJC Scopus subject areas

Statistics and Probability
Condensed Matter Physics

Access to Document

10.1016/j.physa.2016.07.045

Fingerprint Dive into the research topics of 'Magnon-bound-state hierarchy for the two-dimensional transverse-field Ising model in the ordered phase'. Together they form a unique fingerprint.

Cite this

@article{4d1160b424d14f00b69aaea2a50db555,

title = "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, 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.",

keywords = "Exact diagonalization method, Magnon mass gaps, Two-dimensional transverse-field Ising model, Universal amplitude ratio",

author = "Yoshihiro Nishiyama",

note = "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 ).",

year = "2016",

month = dec,

day = "1",

doi = "10.1016/j.physa.2016.07.045",

language = "English",

volume = "463",

pages = "303--309",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",

publisher = "Elsevier",

}

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 ).

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

UR - http://www.scopus.com/inward/record.url?scp=84982671700&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84982671700&partnerID=8YFLogxK

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 -