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Kiyohide Nomura Last modified date:2023.06.12

Associate Professor / condensed matter physics
Department of Physics
Faculty of Sciences

Graduate School

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 Reseacher Profiling Tool Kyushu University Pure
Academic Degree
Ph. D
Country of degree conferring institution (Overseas)
Field of Specialization
Condensed matter physics
ORCID(Open Researcher and Contributor ID)
Total Priod of education and research career in the foreign country
Research Interests
  • Multicritical point of the S=1 XXZ chain withe single ion anisotropy
    keyword : conformal field theory, renormalization
    2021.04Commensurate-incommensurate change.
  • Research on SU(3) quantum spin chain
    keyword : SU(3), conformal field theory, renormalization
    2019.04Commensurate-incommensurate change.
  • Anomaly of susceptibility in the quantum spin models
    keyword : nonlinear susceptibility, Bethe Amsatz, conformal field theory, renormalization
    2017.04Commensurate-incommensurate change.
  • Study of the Ashkin-Teller multicritical point
    keyword : Ashkin-Teller model, antiperiodic boundary condition, conformal field theory, duality
    2016.01Commensurate-incommensurate change.
  • Extension of Lieb-Schultz-Mattis Theorem
    keyword : Lieb-Schultz-Mattis Theorem, U(1) symmetry translational symmetry, frustration, topological aspect
    2014.01Commensurate-incommensurate change.
  • commensurate-incommensurate change
    keyword : AKLT, BLBQ, ANNNI,
    2003.01Commensurate-incommensurate change.
  • Application of the level-spectroscopy method to low dimensional systems
    keyword : conformal field theory, Berezinskii-Kosterlitz-Thouless(BKT) transition renormalization group one-dimensinal quantum system two-dimensinal classical system
    1995.04Low dimensional quantum system.
Academic Activities
1. T.Mashiko, K.Nomura, Critical phenomena around the SU(3) symmetric tricritical point of a spin-1 chain, Phys. Rev. B,, 107, 125406, 2023.03, 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)]. 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..
2. T.Mashiko, K.Nomura, Phase transition of an SU(3) symmetric spin-1 chain, Phys. Rev. B,, 104, 155405, 2021.10, We investigate a phase transition in an SU(3) symmetric spin-1 chain. To study this transition, we numerically diagonalize an SU(3) symmetric Hamiltonian combining the Uimin-Lai-Sutherland (ULS) model Hamiltonian with the Hamiltonian of the exact trimer ground state (Z3 symmetry breaking). Our numerical results are discussed on the basis of the conformal field theory (CFT) and the renormalization group (RG). We then show the phase transition between a trimer liquid phase (massless, no long-range order) and a trimer phase (spontaneously Z3 symmetry breaking). Next, we find the central charge c=2 in the massless phase, and c
3. T.Mashiko, S.Moriya, K.Nomura, Universality Class around the SU(3) Symmetric Point of the Dimer–Trimer Spin-1 Chain, J. Phys. Soc. Jpn.,, 90, 2, 024005, 2021.02, We study critical phenomena of an SU(3) symmetric spin-1 chain when adding an SU(3) asymmetric term. To investigate such phenomena, we numerically diagonalize the dimer–trimer (DT) model Hamiltonian around the SU(3) symmetric point, named the pure trimer (PT) point. We analyze our numerical results on the basis of the conformal field theory (CFT). First of all, we discover that soft modes appear at the wave number q = 0 and ±2π/3 for the PT point, and then the system is critical. Secondly, we find that the system at the PT point can be described by the CFT with the central charge c = 2 and the scaling dimension x = 2/3. Finally, by investigating the eigenvalues of the Hamiltonian in the vicinity of the PT point, we find that there is a phase transition at the PT point from a massive phase to a massless phase. From these numerical results, the phase transition at the PT point belongs to the Berezinskii–Kosterlitz–Thouless (BKT)-like universality class that is explained by the level-1 SU(3) Wess–Zumino–Witten [SU(3)1 WZW] model..
4. N. Aiba, K. Nomura, Method to observe the anomaly of magnetic susceptibility in quantum spin systems, Phys. Rev. B,, 102, 13, 134435, 2020.10, In quantum spin systems, a phase transition is studied from the perspective of magnetization curve and a magnetic susceptibility. We propose a new method for studying the anomaly of magnetic susceptibility χ that indicates a phase transition. In addition, we introduce the fourth derivative A of the lowest-energy eigenvalue per site with respect to magnetization, i.e., the second derivative of χ−1. To verify the validity of this method, we apply it to an S=1/2XXZ antiferromagnetic chain. The lowest energy of the chain is calculated by numerical diagonalization. As a result, the anomalies of χ and A exist at zero magnetization. The anomaly of A is easier to observe than that of χ, indicating that the observation of A is a more efficient method of evaluating an anomaly than that of χ. The observation of A reveals an anomaly that is different from the Kosterlitz-Thouless (KT) transition. Our method is useful in analyzing critical phenomena..
5. S. Moriya, K. Nomura, A New Method to Calculate a 2D Ising Universality Transition Point: Application near the Ashkin–Teller Multicritical Point, J. Phys. Soc. Jpn.,, 89, 9, 093001, 2020.09, We propose a new method to numerically calculate transition points that belongs to 2D Ising universality class for quantum spin models. Generally, near the multicritical point, in conventional methods, a finite size correction becomes very large. To suppress the effect of the multicritical point, we use a z-axis twisted boundary condition and a y-axis twisted boundary condition. We apply our method to an S=1/2 bond-alternating XXZ model. The multicritical point of this model has a BKT transition, where the correlation length diverges singularly. However, with our method, the convergence of calculation is highly improved, thus we can calculate the transition point even near the multicritical point..
6. T. Isoyama K. Nomura, Discrete symmetries and the Lieb–Schultz–Mattis theorem, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptx139, 2017, 10, 103I01, 2017.10, 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..
7. Kiyohide Nomura, Junpei Morishige, Takaichi Isoyama, Extension of the Lieb-Schultz-Mattis theorem, Journal of Physics A: Mathematical and Theoretical, 10.1088/1751-8113/48/37/375001, 48, 37, 2015.09, 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..
8. K. Hijii and K. Nomura, Phase transition of S=1/2 two-leg Heisenberg spin ladder systems with a four-spin interaction, Phys. Rev. B, 10.1103/PhysRevB.80.014426, 80, 1, 014426, 2009.07, 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..
9. T. Murashima and K. Nomura, Incommensurability and edge states in the one-dimensional S=1 bilinear-biquadratic model, Phys. Rev. B, 10.1103/PhysRevB.73.214431, 73, 214431, Vol.73,
p.214431, 2006.06, 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..
10. H. Matsuo and Nomura, Berezinskii-Kosterlitz-Thouless transitions in the six-state
clock model, J. Phys. A, 10.1088/0305-4470/39/12/006, 39, 12, 2953, 2006.03, 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..
11. K. Nomura and T. Murashima, Incommensurability and Edge State in Quantum Spin Chain, J. Phys. Soc. Jpn (Suppl.), 74, 42, Vol. 74 (Suppl.)
pp.42, 2005.01, 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. .
12. K. Nomura, Onset of Incommensurability in Qunatum spin chain, J. Phys. Soc. Jpn, 10.1143/JPSJ.72.476, 72, 3, 476-478, Vol.72, pp.476-478, 2003.03, 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..
13. K. Hijii and K. Nomura, Universality class of an S=1 quantum spin ladder system with four-spin exchange, Phys. Rev. B, 10.1103/PhysRevB.65.104413, 65, 10, 104413, Vol. 65, pp. 104413, 2002.01, 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..
14. S. Hirata and K. Nomura, Phase diagram of S=1/2 XXZ chain with NNN interaction, Phys. Rev. B, 10.1103/PhysRevB.61.9453, 61, 14, 9453-9456, Vol. 61, pp.9453-9456., 2000.01, 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. .
15. K. Nomura and A. Kitazawa, SU(2)/Z_2 symmetry of the BKT transition and twisted boundary condition, J. Phys. A, 10.1088/0305-4470/31/36/008, 31, 36, 7341-7362, Vol. 31, pp.7341-7362, 1998.01, 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..
16. M. Tsukano and K. Nomura, Berezinski-Kosterlitz-Thouless Transition of Spin-1 XXZ Chains
in a staggered Magnetic Field, J. Phys. Soc. Jpn., 10.1143/JPSJ.67.302, 67, 1, 302-306, Vol. 67, pp.302-306, 1998.01.
1. 野村 清英, Multicritical point, conformal field theory and duality, 統計力学セミナー StatPhys Seminar @ UTokyo Hongo, 2020.09, 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).
2. Ashkin-Teller multicritical point and twisted boundary conditions.
3. Anomaly of a magnetic susceptibility in XXZ model for S=1/2 and
comparison with an exact solution.
4. 野村 清英, Extension of the Lieb-­‐Schultz-­‐Mattis and Kolb theorem, STATPHYS26, 2016.07, [URL].
5. Appllication of the LSM theorem to the quantum spin ladder with frustration.
6. 野村 清英, Extension of Lieb-Schultz-Mattis Theorem , ICNS 2015 (Changhua) , 2015.09, [URL].
7. Extension of Lieb-Schultz-Mattis Theorem III.
8. Extension of Lieb-Schultz-Mattis Theorem II.
9. Commensurate-Incommensurate Transition using Complex Analysis.
10. Extension of the Lieb-Schultz-Mattis Theorem.
11. Extension of the Lieb-Schultz-Mattis Theorem.
12. Level Spectroscopy without the Bond-Inversion Symmetry --- In case of an Anisotropic S=1/2 Ladder with Alternating Rung Interactions.