Language：English   Publishing type：Research paper (scientific journal)  

In this study, we consider one-dimensional (1D) quantum spin systems with translation and discrete symmetries (spin reversal, space inversion, and time reversal symmetries). By combining the continuous U(1) symmetry with the discrete symmetries and using the extended Lieb–Schultz–Mattis (LSM) theorem [E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. 16, 407 (1961); K. Nomura, J. Morishige, and T. Isoyama, J. Phys. A 48, 375001 (2015)], we investigate the relation between the ground states, energy spectra, and symmetries. For half-integer spin cases, we generalize the dimer and Néel concepts using the discrete symmetries, and we can reconcile the LSM theorem with the dimer or Néel states, since there was a subtle dilemma. Furthermore, a part of discrete symmetries is enough to classify possible phases. Thus we can deepen our understanding of the relation between the LSM theorem and discrete symmetries.

DOI： 10.1093/ptep/ptx139

Language：English   Publishing type：Research paper (scientific journal)  

Lieb, Schultz and Mattis (LSM) (1961 Ann. Phys., NY 16 407) studied the S = 1/2 XXZ spin chain. The theorems of LSM's paper can be applied to broader models. In the original LSM theorem the nonfrustrating system was assumed. However, reconsidering the LSM theorem, we can extend the LSM theorem for frustrating systems. Next, several researchers tried to extend the LSM theorem for excited states. In the cases , the lowest energy eigenvalues are continuous for wave number q. But we found that their proofs were insufficient, and improve upon them. In addition, we can prove the LSM theory without the assumption of the discrete symmetry, which means that LSM-type theorems are applicable for Dzyaloshinskii-Moriya type interactions or other nonsymmetric models.

DOI： 10.1088/1751-8113/48/37/375001

Language：English   Publishing type：Research paper (scientific journal)  

We study a phase transition and critical properties of the quantum spin ladder system with a four-spin interaction. We determine a phase boundary between a rung singlet and a staggered dimer phases numerically. This phase transition is of a second order in the weak-coupling region. We confirm that this universality class is described by the k=2 SU(2) Wess-Zumino-Witten model, analyzing the central charge and scaling dimensions. In the strong-coupling region, phase transition becomes of a first order.

DOI： 10.1103/PhysRevB.80.014426

Language：English   Publishing type：Research paper (scientific journal)  

Commensurate-incommensurate change on the one-dimensional S=1 bilinear-biquadratic model [H(α)=∑i{Si∙Si+1+α(Si∙Si+1)2}] is examined. The gapped Haldane phase has two subphases (the commensurate Haldane subphase and the incommensurate Haldane subphase) and the commensurate-incommensurate change point (the Affleck-Kennedy-Lieb-Tasaki point, α=1/3). There have been two different analytical predictions about the static structure factor in the neighborhood of this point. By using the Sørensen-Affleck prescription, these static structure factors are related to the Green functions, and also to the energy gap behaviors. Numerical calculations support one of the predictions. Accordingly, the commensurate-incommensurate change is recognized as a motion of a pair of poles in the complex plane.

DOI： 10.1103/PhysRevB.73.214431

Language：English   Publishing type：Research paper (scientific journal)  

A classical 2D clock model is known to have a critical phase with Berezinskii–Kosterlitz–Thouless (BKT) transitions. These transitions have logarithmic corrections which make numerical analysis difficult. In order to resolve this difficulty, one of the authors has proposed a method called 'level spectroscopy', which is based on the conformal field theory. We extend this method to the multi-degenerated case. As an example, we study the classical 2D six-clock model which can be mapped to the quantum self-dual 1D six-clock model. Additionally, we confirm that the self-dual point has a precise numerical agreement with the analytical result, and we argue the degeneracy of the excitation states at the self-dual point from the effective field theoretical point of view.

DOI： 10.1088/0305-4470/39/12/006

Language：English   Publishing type：Research paper (international conference proceedings)  

In quantum spin chains, it has been observed that the incommensurability occurs near valence-bond-solid (VBS) type points. It was difficult to study the commensurate–incommensurate (C–IC) change. On the one hand field theoretical approaches are not justified because of the short correlation length. On the other hand numerical calculations are not suitable to study the incommensurability since it is needed to treat the large size data. We discuss the relation between the edge state and the incommensurability, partially using the previous our study on the C–IC change.

Language：English   Publishing type：Research paper (scientific journal)  

In quantum spin chains, it has been observed that the incommensurability occurs near valence-bond-solid (VBS)-type solvable points, and the correlation length becomes shortest at VBS-type points. In addition, the correlation function decays purely exponentially at VBS-type points, in contrast with the two-dimensional (2D) Ornstein-Zernicke type behavior in other regions with an excitation gap. We propose a mechanism to explain the onset of the incommensurability and the shortest correlation length at VBS-like points. This theory can be applied to more general cases.

DOI： 10.1143/JPSJ.72.476

Language：English   Publishing type：Research paper (scientific journal)  

We study a s=12 Heisenberg spin ladder with four-spin exchange. Combining numerical results with conformal field theory, we find a phase transition with central charge c=32. Since this system has an SU(2) symmetry, we can conclude that this critical theory is described by k=2 SU(2) Wess-Zumino-Witten model with Z2 symmetry breaking.

DOI： 10.1103/PhysRevB.65.104413

Language：English   Publishing type：Research paper (scientific journal)  

We study the ground state properties of one-dimensional XXZ model with next-nearest neighbor coupling alpha and anisotropy Delta. We find the direct transition between the ferromagnetic phase and the spontaneously dimerized phase. This is surprising, because the ferromagnetic phase is classical, whereas the dimer phase is a purely quantum and nonmagnetic phase. We also discuss the effect of bond alternation which arises in realistic systems due to lattice distortion. Our results mean that the direct transition between the ferromagnetic and spin-Peierls phase occur.

DOI： 10.1103/PhysRevB.61.9453

Language：English   Publishing type：Research paper (scientific journal)  

The Berezinskii-Kosterlitz-Thouless (BKT) transition, the transition of the two-dimensional sine-Gordon model, plays an important role in low-dimensional physics. We relate the operator content of the BKT transition to that of the SU(2) Wess-Zumino-Witten model, using twisted boundary conditions. With this method, in order k - 1 to determine the BKT critical point, we can use the level crossing of the lower excitations instead of those for the periodic boundary case, thus the convergence to the transition point is highly improved. We verify the efficiency of this method by applying it to the S = 1, 2 spin chains.

DOI： 10.1088/0305-4470/31/36/008

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1143/JPSJ.67.302

Publisher：Physical Review B  

We investigate critical phenomena of a spin-1 chain in the vicinity of the SU(3) symmetric critical point, which we already specified in a previous study [Mashiko and Nomura, Phys. Rev. B 104, 155405 (2021)10.1103/PhysRevB.104.155405]. We numerically diagonalize a Hamiltonian combining the bilinear-biquadratic Hamiltonian with the trimer Hamiltonian. We then discuss the numerical results based on the conformal field theory and the renormalization group. As a result, we first verify that the critical point found in our previous study is the tricritical point among the Haldane phase, the trimer phase, and the the trimer-liquid (TL) phase. Second, with regard to the TL-trimer transition and the TL-Haldane transition, we find that the critical phenomena around this tricritical point belong to the Berezinskii-Kosterlitz-Thouless-like universality class. Third, we find the boundary between the Haldane phase and the trimer phase, which is illustrated by the massive self-dual sine-Gordon model.

DOI： 10.1103/PhysRevB.107.125406

Web of Science

Scopus

Language：English   Publishing type：Research paper (international conference proceedings)  

We numerically investigate the ground-state phase diagram of an S = 2 quantum
spin chain with the XXZ and on-site anisotropies described by
H =Σj (Sxj Sxj+1 +Syj Syj+1 +ΔSzj Szj+1) + DΣj (Szj )2,
where Δ denotes the XXZ anisotropy parameter of the nearestneighbor
interactions and D the on-site anisotropy parameter. We restrict ourselves to the
Δ > 0 and D > 0 case for simplicity. Our main purpose is to obtain the definite conclusion
whether there exists or not the intermediate-D (ID) phase, which was proposed by Oshikawa
in 1992 and has been believed to be absent since the DMRG studies in the latter half of 1990’s.
In the phase diagram with Δ > 0 and D > 0 there appear the XY state, the Haldane state,
the ID state, the large-D (LD) state and the N´eel state. In the analysis of the numerical data
it is important to distinguish three gapped states; the Haldane state, the ID state and the LD
state. We give a physical and intuitive explanation for our level spectroscopy method how to
distinguish these three phases.

DOI： 10.1088/1742-6596/320/1/012018

Language：English   Publishing type：Research paper (scientific journal)  

Using mainly numerical methods, we investigate the ground-state phase diagram of the S = 2 quantum spin chain described by H = ∑ j ( S j x S j +1 x + S j y S j +1 y + Δ S j z S j +1 z ) + D ∑ j ( S j z ) 2 , where Δ denotes the X X Z anisotropy parameter of the nearest-neighbor interactions and D the on-site anisotropy parameter. We restrict ourselves to the case of Δ≥0 and D ≥0 for simplicity. Each of the phase boundary lines is determined by the level spectroscopy or the phenomenological renormalization analysis of numerical results of exact-diagonalization calculations. The resulting phase diagram on the Δ– D plane consists of four phases; the X Y 1 phase, the Haldane/large- D phase, the intermediate- D phase, and the Néel phase. The remarkable natures of the phase diagram are as follows: (1) there exists an intermediate- D phase which was predicted by Oshikawa in 1992; (2) the Haldane state and the large- D state belong to the same phase; (3) the shape of the phase diagram on the Δ– D plane is different from that considered so far. We note that this is the first report on the observation of the intermediate- D phase.

DOI： 10.1143/JPSJ.80.043001

Language：English   Publishing type：Research paper (international conference proceedings)  

We numerically investigate the magnetization process of a frustrated S=1 chain with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) exchange interactions, which compete with each other, and also with uniaxial single-ion-type anisotropy energies. Special attention is paid to the half magnetization plateau which appears at the half of the saturation magnetization in the ground-state magnetization curve. We determine the parameter region where this plateau appears by employing the level spectroscopy method, and find that the plateau appears even in the absence of the single-ion-type anisotropy, if the ratio of the nnn to the nn interaction constant is in a specified region.

DOI： 10.1088/1742-6596/200/2/022065

Language：English   Publishing type：Research paper (scientific journal)  

We investigate infinite-order phase transitions like the Berezinskii–Kosterlitz–Thouless transition observed in a triangular-lattice three-spin interaction model. Based on a field theoretical description and the operator-production-expansion technique, we perform the renormalization-group analysis, and then clarify properties of marginal operators near the phase transition points. The results are utilized to establish criteria to determine the transition points and some universal relations among excitation levels to characterize the transitions. We verify these predictions via the numerical analysis on eigenvalue structures of the transfer matrix. Also, we discuss an enhancement of symmetry at the end points of a critical intermediate phase in connection with a transition observed in the ground state of the bilinear-biquadratic spin-1 chain.

DOI： 10.1088/1751-8113/41/37/375001

Language：English   Publishing type：Research paper (scientific journal)  

In several frustrated systems, incommensurate behaviours are often observed. For the S = 1 bilinear–biquadratic model, we show that the main oscillatory behaviour, which is proportional to the free edge spins, is eliminated in the incommensurate subphase, considering the average of triplet and singlet energy spectra under open boundary conditions. In the same way, the π-mode oscillation is also removed in the commensurate subphase. Moreover, we find that higher-order corrections are exponentially decaying from an analysis of small-size data.

DOI： 10.1088/0953-8984/19/14/145210

Language：English   Publishing type：Research paper (scientific journal)  

We investigate the triangular-lattice antiferromagnetic Ising model with a spatially anisotropic next-nearest-neighbor ferromagnetic coupling, which was first discussed by Kitatani and Oguchi. By employing the effective geometric factor, we analyze the scaling dimensions of the operators around the Berezinskii-Kosterlitz-Thouless (BKT) transition lines, and determine the global phase diagram. Our numerical data exhibit that two types of BKT-transition lines separate the intermediate critical region from the ordered and disordered phases, and they do not merge into a single curve in the antiferromagnetic region. We also estimate the central charge and perform some consistency checks among scaling dimensions in order to provide the evidence of the six-state clock universality. Further, we provide an analysis of the shapes of boundaries based on the crossover argument.

DOI： 10.1103/PhysRevE.74.011104

Language：English   Publishing type：Research paper (scientific journal)  

We attempt to construct U(1) conformal field theory (CFT) in the Tomonaga–Luttinger (TL) liquid with the 1/rβ long-range interaction (LRI). Treating the long-range forward scattering as a perturbation and applying CFT to it, we derive finite size scalings which depend on the power of the LRI. The obtained finite size scalings give nontrivial behaviours when β is odd and is close to 2. We find consistency between the analytical arguments and numerical results in the finite size scaling of energy.

DOI： 10.1088/0305-4470/39/9/012

Language：English   Publishing type：Research paper (scientific journal)  

The one dimensional S =1 XXZ model with next-nearest-neighbor interaction α and Ising-type anisotropy Δ is studied by using a numerical diagonalization technique. We discuss the ground state phase diagram of this model numerically by the twisted-boundary-condition level spectroscopy method and the phenomenological renormalization group method, and analytically by the spin wave theory. We determine the phase boundaries among the XY phase, the Haldane phase, the ferromagnetic phase and the Néel phase, and then we confirm the universality class. Moreover, we map this model onto the non-linear σ model and analyze the phase diagram in the α-1 and Δ1 region by using the renormalization group method.

DOI： 10.1143/JPSJ.74.1544

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1103/PhysRevE.72.046103

Language：English   Publishing type：Research paper (scientific journal)  

We investigate the ground-state phase diagram of the S=12 two-leg XXZ spin-ladder system with an isotropic interchain coupling. In this model, there is the Berezinskii-Kosterlitz-Thouless transition which occurs at the XY-Haldane and XY-rung singlet phase boundaries. It was difficult to determine the transition line using traditional methods. We overcome this difficulty using the level spectroscopy method combined with the twisted boundary condition method, and we check the consistency. We find out that the phase boundary between XY phase and Haldane phase lies on Δ=0 line. And we show that there exist two different XY phases, which we can distinguish investigating a XX correlation function.

DOI： 10.1103/PhysRevB.72.014449

Language：English   Publishing type：Research paper (scientific journal)  

We show that the one-dimensional spin-1 XY model has an additional SU(2) symmetry for the open boundary condition and for an artificial one. We can explain some degeneracies of excitation states which were reported in previous numerical studies.

DOI： 10.1088/0305-4470/36/23/104

Language：English   Publishing type：Research paper (scientific journal)  

We study an S=12 quantum-spin ladder system with four-spin cyclic exchange, using the density matrix renormalization group (DMRG) and exact diagonalization methods. Recently, the phase transition and its universality class in this system have been studied. However, controversies remain on whether the phase transition is second-order type or another type and on the nature of critical phenomena. In addition, there are several arguments concerning where the transition point is. Analyzing DMRG data, we use an approach to determine the ordered phase which appears after the phase transition. We find that the edge state appears under the open boundary condition by investigating excitation energies of states with higher magnetizations. We also estimate the correlation length and discuss the critical behavior.

DOI： 10.1103/PhysRevB.68.134403

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/S0375-9601(99)00544-7

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1103/PhysRevB.59.11358

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1103/PhysRevB.60.7850

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1103/PhysRevB.57.R8087

Event date： 2023.2

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：福井大学　遠赤外領域開発研究センター   Country：Japan  

Event date： 2022.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東京工業大学   Country：Japan  

Event date： 2022.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東京工業大学   Country：Japan  

Event date： 2022.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2021.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2021.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2021.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2021.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2021.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2021.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2020.12

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2020.12

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2020.9

Language：English   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Critical phenomena are one of the important subjects in condensed matter physics.
Many developments about critical phenomena,
such as renormalization group, numerical methods etc. have been done.
But, when the model has a multicritical point, the scaling behaviors become
difficult due to the interference of multiple critical lines.
So, conventional numerical methods are not useful near a multicritical point.

We have studied several multicritical phenomena combining
with the conformal field theory and numerical methods (level spectroscopy etc) [1,2].
And we discuss the relation with the duality,
such as the Kramers-Wannier duality and the Ashkin-Teller self-duality [2].

[1] A.Kitazawa and K.N.: Phys. Rev. B 59, 11358

[2] S. Moriya and K. N: J. Phys. Soc. Jpn. 89, 093001 (2020)

Event date： 2020.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2020.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2020.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2020.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：名古屋大学（東山キャンパス）   Country：Japan  

Event date： 2020.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：名古屋大学（東山キャンパス）   Country：Japan  

Event date： 2020.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：名古屋大学（東山キャンパス）   Country：Japan  

Event date： 2020.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：名古屋大学（東山キャンパス）   Country：Japan  

Event date： 2020.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：名古屋大学（東山キャンパス）   Country：Japan  

Event date： 2020.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：名古屋大学（東山キャンパス）   Country：Japan  

Event date： 2019.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：岐阜大学   Country：Japan  

ひねり境界条件は、レベルスペクトロスコピー法で　BKT 転移の相境界決定に
使われる他、輸送現象でも重要である。
これについて　Lieb-Schultz-Mattis の定理の拡張を試みる。

Event date： 2019.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：岐阜大学   Country：Japan  

Event date： 2019.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：岐阜大学   Country：Japan  

Event date： 2019.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：岐阜大学   Country：Japan  

Event date： 2019.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：九州大学 伊都キャンパス   Country：Japan  

Event date： 2019.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：九州大学 伊都キャンパス   Country：Japan  

Anomaly of a magnetic susceptibility in XXZ model for S=1/2 and
comparison with an exact solution

Event date： 2019.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：九州大学 伊都キャンパス   Country：Japan  

Ashkin-Teller multicritical point and twisted boundary conditions

Event date： 2018.10 - 2019.11

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：京都大学 基礎物理学研究所   Country：Japan  

Event date： 2018.10 - 2019.11

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：京都大学 基礎物理学研究所   Country：Japan  

Event date： 2018.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東京理科大学（野田キャンパス）   Country：Japan  

Event date： 2018.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東京理科大学（野田キャンパス）   Country：Japan  

量子スピン系における磁化率ではエネルギーギャップの有無が重要な要素となっている。その先
行研究として、 2 次元量子スピン系ではエネルギーギャップの有無に関わらず、磁化 0 における磁
化率に異常が見られることが報告されている\cite{Sakai-Nakano-2016}。
また、 Bethe 仮説による厳密解を用いた場合に
おいても磁化率の異常性は確認されている。しかし、その異常については非線形磁化率などを用い
た研究が不十分のため、詳細に調べる価値があると判断される。

本研究では 1 次元量子スピン系において磁化率を数値的に調べた。
1次元かつエネルギーギャップがない場合について、追い詰めた研究は不十分で
ある。 (エネルギー
ギャップがある場合は先行研究が存在する\cite
{Takahashi-Sakai-1991, Sakai-Takahashi-1991}
) 。
磁化率は磁化 0 で尖って見え
るため、磁化率とエネルギー、非線形磁化率の関係性から、エネルギーの 3,4 階微分と非線形磁化
率について数値的に調べた。
その異常性について詳しく解析した結果、異方性パラメータ
の値によっては非線形磁化率の発散が見られた。

\begin{thebibliography}{99}
\bibitem{Sakai-Nakano-2016}
T. Sakai and H. Nakano,Quantum Spin Fluid in S=1/2 Kagome-Lattice
Antiferromagnet-Spin Gap Issue(Gapless)- at STATPHYS(2016)
\bibitem{Takahashi-Sakai-1991}
M. Takahashi and T. Sakai,J.Phys.Soc.Jpn.60,pp.760-763(1991)
\bibitem{Sakai-Takahashi-1991}
T. Sakai and M. Takahashi,Phys.Rev.B43,13383(1991)
\end{thebibliography}

Event date： 2017.12

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：研究会会場：みのお山荘　風の杜   Country：Japan  

Event date： 2017.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：大阪大学（豊中キャンパス）   Country：Japan  

Event date： 2017.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：大阪大学（豊中キャンパス）   Country：Japan  

Event date： 2017.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：大阪大学（豊中キャンパス）   Country：Japan  

LSM 的な方法で構成される基底状態の候補としてはdimer的なものやN\'eel的なものがあり、これらは離散的対称性（スピン反転対称性や空間反転対称性、時間反転対称性）によって特徴づけられる。その過程にはnormalizationの議論が必要だったことを示した。加えて、限定的な離散的対称性でもこの議論が可能であることやその応用としてmagnetic plateau の場合についても述べる予定である。

Event date： 2016.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：金沢大学 （角田キャンパス）   Country：Japan  

転移点を数値的に精度よく決定することは臨界指数の計算で重要になる。しかし、一般に多重
臨界点近傍では対数補正のため旧来の有限サイズスケーリング法がうまく機能せず、転移点を精
確に決定する一般的な方法はない。本発表では一例として S = 1/2 ボンド交代 XXZ スピン鎖の
多重臨界点を扱う。ハミルトニアンは以下で与えられる

この模型は隠れた Z 2 × Z 2 対称性を持ち、 1 次元量子 Ashkin-Teller 模型 (AT 模型 ) に等価であ
ることが知られている [1] 。 ∆ − δ 相図は BKT 転移 (XY-dimer) 、 Gaussian 転移 (dimer-dimer
転移 ) 、 2D Ising 転移 (dimer-Néel) から成り、 Gaussian 転移線は 2 本の 2D Ising 転移線に分か
れ 3 重臨界点を作っている。この Néel-dimer 多重臨界点は SU(2) 対称な点 (δ, ∆) = (0, 1) だろ
うと考えられているが数値計算で追い詰めた研究はまだない ( 有限サイズスケーリングによる先行
研究はある [2]) 。そこで Gaussian 転移で有効な z 軸まわりのひねり境界条件法 [3] から着想を得
て、 y 軸まわりのひねり境界条件法を考え多重臨界点近傍の相転移を数値的に調べた。その結果、
有限サイズスケーリングに比べて y 軸まわりのひねり境界条件法の方がサイズ依存性が小さいこ
とがわかった。
また、この方法の理論的正当性についても考察した。この多重臨界点は隠れた Z 2 × Z 2 対称性
に関連することが知られているが、先行研究では開境界条件の場合しか調べられていなかった。
そこで PBC や yTBC でも (1) は隠れた Z 2 × Z 2 対称性を持つかを調べた。結果として、 (1) を
AT 模型に変換する演算子が non-local であることから、エッジからおつりの項が出ることが分
かった (1 次元量子 XY 模型を Jordan-Wiegner 変換で解くときにも似た状況が現れる ) 。そして、
このお釣りの項は Z 2 × Z 2 対称性を破らないことを確かめた。
参考文献
[1] M. Kohmoto, M. den Nijs, and L. P. Kadanoff, Phys. Rev. B 24, 5229 (1981).
[2] H. Nishimori, K. Okamoto and M. Yokozawa, J. Phys. Soc. Jpn. 56, 4126 (1987).
[3] A.Kitazawa, J. Phys. A: Math. Gen. 30 285 (1997).

Event date： 2016.7

Language：English   Presentation type：Oral presentation (general)  

Venue：Lyon   Country：France  

Other Link： http://statphys26.sciencesconf.org/

Event date： 2016.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東北学院大学（泉キャンパス）   Country：Japan  

Appllication of the LSM theorem to the quantum spin ladder with frustration

Event date： 2016.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東北学院大学（泉キャンパス）   Country：Japan  

Event date： 2016.3 - 2015.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東北学院大学（泉キャンパス）   Country：Japan  

Event date： 2015.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：関西大学 (千里山キャンパス)   Country：Japan  

格子上の量子多体スピン系では , エネルギースペクトルが取りうる可能性として , (a) 基底状態と連続スペクトルの間にエネルギーギャップがある場合 (b) 基底状態と連続スペクトルが繋がっている場合 の 2 つがある . スピン反転操作には x;y;z 軸周りの 3 種類のものが考えられるが , これらをひとつの組として 考えることで ,3 種のスピン反転演算子の固有値の組がとる値に制限を加える事が出来る . このことと Lieb-Schultz-Mattis の定理 [1][2] を結びつけることで , 今回はこの (a) について制 限をつけることができた . 具体的には , 問題設定として 並進対称性をもつ一次元スピン系 ハミルトニアンは一次元 XXZ モデル (SU(2) 対称性があるときは XXX) 周期的境界条件 短距離相互作用 系の長さは偶数 を取り , 基底状態と連続スペクトルとの間にエネルギーギャップがあるとすれば , 対応する物理的 な状態としては dimer 的状態しかとりえないことを示した . また , 他モデルへの応用として , ほぼ同じ手順で Spin Ladder,Spin Tube[3][4] の場合を考える ことが出来る .

Event date： 2015.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：関西大学 (千里山キャンパス)   Country：Japan  

量子1次元スピン系の Lieb-Schultz-Mattis の定理
\cite{Lieb-Schultz-Mattis-1961}
の拡張について議論する．
LSM の第2定理を整理し直したところ，定理の前提条件としては
\begin{itemize}
\item U(1) 対称性
\item 並進対称性
\item 短距離相互作用
\end{itemize}
の3つで十分であることが分かった．
結論は
\begin{itemize}
\item 磁化が有理数の特定の場合を除くと，
エネルギースペクトルの最低値は波数に対して連続である．
\item エネルギースペクトルの最低値は波数に対して(磁化により定まる)周期性を持つ
\end{itemize}
\cite{Nomura-Morishige-Isoyama}
である．

基底状態が唯一と言う前提条件は不必要であることが分かった．
したがってフラストレーションのある系にも応用できる．
また，空間反転対称性やスピン反転対称性なしでも定理を
示すことができるので，ジャロシンスキー守谷相互作用などを含む
場合にも使うことができる．

Event date： 2015.9

Language：English   Presentation type：Oral presentation (general)  

Venue：National Changhua University of Education   Country：Taiwan, Province of China  

Lieb, Schultz and Mattis (LSM)
\cite{Lieb-Schultz-Mattis-1961}
studied the S=1/2 XXZ spin chain.
The theorems of LSM's paper can be applied to broader models.
In the original LSM theorem the nonfrustrating system was assumed.

However, reconsidering the LSM theorem, we can extend the LSM theorem
for frustrating system \cite{Nomura-Morishige-Isoyama-2015}s.
Next, several researchers tried to extend the LSM theorem
for excited states.
In the cases $S^{z}_{T} = \pm 1,\pm 2 \cdots$, the lowest energy
eigenvalues are continuous for wave number $q$.
But we found that their proofs were insufficient, and improve upon them.
In addition, we can prove the LSM theory without the assumption of the
discrete symmetry, which means that the LSM-type theorems
are applicable for
Dzyaloshinskii-Moriya type interactions or other nonsymmetric models.

Other Link： http://science.ncue.edu.tw/icns2015/

Event date： 2015.3 - 2014.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：早稲田大学 早稲田キャンパス   Country：Japan  

Extension of Lieb-Schultz-Mattis Theorem III

Event date： 2015.3 - 2014.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：早稲田大学 早稲田キャンパス   Country：Japan  

Commensurate-Incommensurate Transition using Complex Analysis

Event date： 2015.3 - 2014.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：早稲田大学 早稲田キャンパス   Country：Japan  

Extension of Lieb-Schultz-Mattis Theorem II

Event date： 2015.1

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：福井大学 遠赤外領域開発研究センター   Country：Japan  

Event date： 2015.1

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：福井大学 遠赤外領域開発研究センター   Country：Japan  

Event date： 2014.12

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：崇城大学 (熊本)   Country：Japan  

量子系のS=1/2 next-nearest-neighbour chain、S=1 bilinear-biquadratic chain のエネルギー固
有値、相関関数を調べる。これらのモデルでは、秩序相におけるオーダーの周期と格子の周期の比
が有理数である整合領域と無理数である非整合領域の間の遷移が確認されている。転移点近傍では
相関長がとても短く、連続極限をとって考えることは適切でない。そのため、この整合ー非整合遷
移(C-IC 遷移) について複素関数論の観点から考察することで、調べていく。それぞれの領域での
C-IC 遷移の相関関数を統一的に扱うために構造因子を定義する。構造因子は同時刻相関を表して
おり、グリーン関数と対応づけることが出来る。グリーン関数の対称性、特異点の性質から整合領
域、非整合領域、転移点であるdisordered point での極と零点の構造に制限がつき、ある程度の関
数形を見積もることができた。
参考文献
[1] U.Schollw¨ock, Th.Jolicoeur,and T.Garel: Phys.Rev.B 53,(1996),3304.
[2] Fath and S¨ut¨o: Phys.Rev.B 62,(2000),3778.
[3] T.Murashima, K.Nomura: Phys.Rev.B 73,(2006),214431.

Event date： 2014.12

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：崇城大学 (熊本)   Country：Japan  

Extension of the Lieb-Schultz-Mattis Theorem

Event date： 2014.9 - 2014.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：中部大学　春日井キャンパス   Country：Japan  

Extension of the Lieb-Schultz-Mattis Theorem

Event date： 2014.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：中部大学 春日井キャンパス   Country：Japan  

Level Spectroscopy without the Bond-Inversion Symmetry --- In case of an Anisotropic S=1/2 Ladder with Alternating Rung Interactions

Event date： 2014.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東海大学 湘南キャンパス   Country：Japan  

講演題目のラダー系はサイト反転に対して対称である．
ところで，Kitazawa により提案されたひねり境界条件法は
ガウシアン転移や BKT 転移を決めるのに大変有効な方法であるが，
実はボンド反転に対して対称な系でのみ定義されていた．
サイト反転に対して対称な系でもひねり境界条件法が使えるように
拡張する．

Event date： 2013.12

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：福井大学 遠赤外領域開発研究センター   Country：Japan  

Event date： 2012.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：横浜国立大学常盤台キャンパス   Country：Japan  

Event date： 2012.2

Presentation type：Oral presentation (general)  

Venue：福井大学   Country：Japan  

Event date： 2011.8

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Venue：Pukyong National University   Country：Korea, Republic of  

Event date： 2011.3

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Venue：新潟大学   Country：Japan  

Event date： 2010.12

Presentation type：Oral presentation (general)  

Venue：福井大学   Country：Japan  

Event date： 2010.12

Presentation type：Oral presentation (general)  

Venue：長崎大学   Country：Japan  

Event date： 2010.9

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Venue：大阪府立大学   Country：Japan  

Event date： 2010.3

Presentation type：Oral presentation (general)  

Venue：岡山大学   Country：Japan  

Event date： 2010.3

Presentation type：Oral presentation (general)  

Venue：岡山大学   Country：Japan  

Event date： 2010.3

Presentation type：Oral presentation (general)  

Venue：岡山大学   Country：Japan  

Event date： 2010.3

Presentation type：Oral presentation (general)  

Venue：岡山大学   Country：Japan  

Event date： 2010.3

Presentation type：Oral presentation (general)  

Venue：横浜市   Country：Japan  

Event date： 2010.3

Presentation type：Oral presentation (general)  

Venue：横浜市   Country：Japan  

Event date： 2010.3

Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2010.2

Presentation type：Oral presentation (general)  

Venue：SPring-8   Country：Japan  

Event date： 2010.1

Presentation type：Oral presentation (general)  

Venue：八王子セミナーハウス   Country：Japan  

Event date： 2010.1

Presentation type：Oral presentation (general)  

Venue：八王子セミナーハウス   Country：Japan  

Event date： 2009.12

Presentation type：Oral presentation (general)  

Venue：宮崎大学   Country：Japan  

Event date： 2009.12

Presentation type：Oral presentation (general)  

Venue：宮崎大学   Country：Japan  

Event date： 2009.12

Presentation type：Oral presentation (general)  

Venue：宮崎大学   Country：Japan  

Event date： 2009.1

Presentation type：Symposium, workshop panel (public)  

Venue：Honoluku   Country：United States  

Event date： 2008.3 - 2009.3

Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2008.3

Presentation type：Oral presentation (general)  

Venue：近畿大学   Country：Japan  

Event date： 2021.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2020.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンラインで実施   Country：Japan  

Event date： 2015.11

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東大物性研究所本館6階大講義室（A632)   Country：Japan  

量子1次元スピン系でのLieb-Schultz-Mattisの定理
[1]およびKolbの議論[2]の拡張について議論する．
LSMの第2定理を整理し直したところ，定理の前提条件としては

U(1)対称性

並進対称性

短距離相互作用
の3つで十分であることが分かった．結論は

磁化が有理数となる場合を除くと，エネルギースペクトルの最低値は波数
qについて連続である．

エネルギースペクトルの最低値は，波数に対して
(磁化により定まる)
周期性を持つ
[3]
である．
基底状態が唯一と言う前提条件は不必要であることが分かった．したがってフラストレーショ
ンのある系にも応用できる．また，空間反転対称性やスピン反転対称性なしでも定理を示すこと
ができるので，ジャロシンスキー守谷相互作用などを含む場合にも使うことができる．
これにより，近似や数値計算などに制約を付けることができる

Event date： 2014.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：中部大学　春日井キャンパス   Country：Japan  

Ground State of an Anisotropic S=1/2 Ladder with Alternating Rung Interactions IV

Event date： 2014.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東海大学 湘南キャンパス   Country：Japan  

Event date： 2012.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：横浜国立大学常盤台キャンパス   Country：Japan  

Event date： 2012.3

Presentation type：Oral presentation (general)  

Venue：関西学院大学   Country：Japan  

Event date： 2011.11

Presentation type：Oral presentation (general)  

Venue：Yukawa Institute for Theoretical Physics (YITP)   Country：Japan  

Event date： 2011.9

Presentation type：Oral presentation (general)  

Venue：富山大学   Country：Japan  

Event date： 2011.9

Presentation type：Oral presentation (general)  

Venue：富山大学   Country：Japan  

Event date： 2011.7

Venue：彦根市   Country：Japan  

Event date： 2011.3

Presentation type：Oral presentation (general)  

Venue：新潟大学   Country：Japan  

Event date： 2011.3

Presentation type：Oral presentation (general)  

Venue：新潟大学   Country：Japan  

Event date： 2010.1

Presentation type：Oral presentation (general)  

Venue：福井県敦賀市西公民館   Country：Japan  

Event date： 2009.12

Presentation type：Oral presentation (general)  

Venue：宮崎大学   Country：Japan  

Event date： 2008.3 - 2003.3

Venue：近畿大学   Country：Japan  

Presentation type：Oral presentation (general)  

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：1

Type：Competition, symposium, etc. 

Number of participants：4,000

Type：Peer review 

Number of peer-reviewed articles in Japanese journals：1

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：1

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：1

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：2

Type：Competition, symposium, etc. 

Type：Competition, symposium, etc. 

Type：Competition, symposium, etc. 

Type：Competition, symposium, etc. 

Type：Competition, symposium, etc. 

Audience：Infants,　Schoolchildren,　Junior students,　High school students

Type：Seminar, workshop

Audience：Infants,　Schoolchildren,　Junior students,　High school students

Type：Seminar, workshop