一次元 S=1 量子スピン系の SU(3)対称な三重臨界点近傍での臨界現象

概要

九州大学学術情報リポジトリ
Kyushu University Institutional Repository

Critical phenomena in the vicinity of the SU(3)
symmetric tri-critical point of a spin-1 chain
益子, 通生流

https://hdl.handle.net/2324/6787404
出版情報：Kyushu University, 2022, 博士（理学）, 課程博士
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（様式３）

氏

名

：益子

論 文 名

：

区

：

分

通生流

Critical phenomena in the vicinity of the SU(3) symmetric tri-critical point
of a spin-1 chain
(一次元 S=1 量子スピン系の SU(3)対称な三重臨界点近傍での臨界現象)
甲
論

文

内

容

の

要

旨

Critical phenomena in low dimensional and continuously symmetric quantum systems have been
important research subjects, where strong quantum fluctuation causes a variety of non-trivial physical
properties. In the SU(3) symmetric case, several researchers have tried to reveal the critical properties,
although with conventional numerical methods, it has been difficult to deal with it, due to the logarithmic
corrections. In our works, we investigate the critical phenomena near the SU(3) symmetric critical point
by numerically diagonalizing the Hamiltonian of a spin-1 chain
�trimer
� ≡ cos 𝜙𝜙 𝐻𝐻
�BLBQ + sin 𝜙𝜙 𝐻𝐻
𝐻𝐻

In the above equation, we combine the bilinear-biquadratic (BLBQ) Hamiltonian with the trimer
Hamiltonian. We analyze numerical results utilizing the perturbative renormalization group of the
conformal field theory (CFT) to overcome the logarithmic corrections. We then obtain conclusions both
in the SU(3) symmetric case and non-SU(3) symmetric case as follows.
Firstly, for the SU(3) symmetric system, we find the phase transition between a massless trimer liquid
(TL) phase and a long-range ordered trimer phase. We then calculate the critical exponents, the central
charge c and the scaling dimension x. From these numerical results, we identify that the universality
class of the TL phase is illustrated with the level-1 SU(3) Wess–Zumino–Witten [SU(3)1 WZW] model.
Secondly, we performed numerical calculations expanding to the non-SU(3) symmetric case. We here
confirm that the SU(3) symmetric critical point is the tri-critical point among the TL phase, the trimer
phase, and the Haldane phase. For the TL–trimer transition and TL–Haldane transition, we specify that
the critical phenomena around this tri-critical
point belong to the same universality class as
that of the SU(3)1 WZW model. Moreover, we
find that the boundary between the Haldane
phase and the trimer phase is explained with the
self-dual sine-Gordon (SDSG) model of the
massive

spin

current. These

results

are

applicable to experiments of ultracold SU(ν)
symmetric atomic systems in an optical lattice.
Fig. 1. Phase diagram around the SU(3) symmetric
tri-critical point.