研究者総覧

中村 正明 (ナカムラ マサアキ)

  • 大学院理工学研究科 数理物質科学専攻 准教授
Last Updated :2020/11/10

研究者情報

学位

  • 博士(理学)(東京工業大学)

ホームページURL

J-Global ID

研究キーワード

  • 低次元強相関系   トポロジカル絶縁体   量子ホール効果   

研究分野

  • 自然科学一般 / 数理物理、物性基礎

経歴

  • 2015年10月 - 現在  愛媛大学大学院理工学研究科数理物質科学専攻准教授
  • 2013年04月 - 2015年09月  東京大学生産技術研究所Institute of Industrial Science特任研究員
  • 2013年05月 - 2014年04月  マックス・プランク研究所 (Stuttgart)研究員
  • 2009年02月 - 2013年03月  東京工業大学大学院理工学研究科 物性物理学専攻 大学院理工学研究科 物性物理学専攻特任准教授
  • 2008年04月 - 2009年02月  マックス・プランク研究所 (Dresden)客員研究員
  • 2001年04月 - 2008年03月  東京理科大学理学部第一部応用物理学科助手(助教)
  • 2000年04月 - 2001年03月  マックス・プランク研究所 (Dresden)客員研究員
  • 1998年07月 - 2000年03月  東京大学 物性研究所物性理論研究部門 高橋實研究室中核的研究機関研究員(COE研究員)
  • 1998年04月 - 1998年07月  東京大学 物性研究所物性理論研究部門 高橋實研究室研究生

学歴

  • 1995年04月 - 1998年03月   東京工業大学大学院   理工学研究科   物理学専攻博士課程
  • 1993年04月 - 1995年03月   慶應義塾大学大学院   理工学研究科   物理学専攻修士課程
  • 1989年04月 - 1993年04月   慶應義塾大学   理工学部   物理学科

所属学協会

  • アメリカ物理学会   日本物理学会   

研究活動情報

論文

  • Exact Plaquette-Ordered Ground States with Exact Edge States of the Generalized Hubbard Model in Corner Sharing Lattices
    N. Nakatsuji, S. Nishimoto, M. Nakamura
    arXiv:2008.11599 2020年08月 [査読有り]
  • 古谷 峻介, 中村 正明
    Physical Review B 99 144426  2019年04月 [査読有り]
     研究論文(学術雑誌)
  • 中村 正明, 古谷 峻介
    Physical Review B 99 075128  2019年02月 [査読有り]
  • 中村 正明, 西本 理
    The European Physical Journal B 91 203  2018年 [査読有り][招待有り]
     研究論文(学術雑誌)
  • Makiko Okada, Hidekazu Tanaka, Nobuyuki Kurita, Kohei Johmoto, Hidehiro Uekusa, Atsushi Miyake, Masashi Tokunaga, Satoshi Nishimoto, Masaaki Nakamura, Marcelo Jaime, Guillaume Radtke, Andres Saul
    PHYSICAL REVIEW B 94 9 094421-1 - 8 2016年09月 [査読有り]
     研究論文(学術雑誌) 
    We synthesized single crystals of composition Ba2CuSi2O6Cl2 and investigated their quantum magnetic properties. The crystal structure is closely related to that of the quasi-two-dimensional (2D) dimerized magnet BaCuSi2O6 also known as Han purple. Ba2CuSi2O6Cl2 has a singlet ground state with an excitation gap of Delta/k(B) = 20.8 K. The magnetization curves for two different field directions almost perfectly coincide when normalized by the g factor except for a small jump anomaly for a magnetic field perpendicular to the c axis. The magnetization curve with a nonlinear slope above the critical field is in excellent agreement with exact-diagonalization calculations based on a 2D coupled spin-dimer model. Individual exchange constants are also evaluated using density functional theory (DFT). The DFT results demonstrate a 2D exchange network and weak frustration between interdimer exchange interactions, supported by weak spin-lattice coupling implied from our magnetostriction data. The magnetic-field-induced spin ordering in Ba2CuSi2O6Cl2 is described as the quasi-2D Bose-Einstein condensation of triplets.
  • Masaaki Nakamura, Akiyuki Tokuno
    PHYSICAL REVIEW B 94 8 081411(R)-1 - 5 2016年08月 [査読有り]
     研究論文(学術雑誌) 
    We discuss dynamic spin susceptibility (DSS) in two-dimensional (2D) Dirac electrons with spin-orbit interactions to characterize topological insulators. The imaginary part of the DSS appears as an absorption rate in response to a transverse ac magnetic field, just as in an electron spin resonance experiment for localized spin systems. We found that when the system is in a static magnetic field, the topological state can be identified by an anomalous resonant peak of the imaginary part of the DSS as a function of the frequency of the transverse magnetic field omega. In the absence of a static magnetic field, the imaginary part of the DSS becomes a continuous function of omega with a threshold frequency omega(c). In this case, the topological and the trivial phases can also be distinguished by the values of omega(c) and by the line shapes. Thus the DSS is an experimentally observable physical quantity to characterize a topological insulator directly from bulk properties, without observing a topological transition.
  • Satoshi Nishimoto, Masaaki Nakamura
    Physical Review B - Condensed Matter and Materials Physics 92 14 2015年10月 [査読有り]
     研究論文(学術雑誌) 
    The S=1 antiferromagnetic Heisenberg model on a kagome lattice is studied using the density-matrix renormalization-group method. To identify the ground state, we take four kinds of clusters into account periodic, cylindrical, and two open ones. The hexagonal-singlet solid (HSS) and triangular valence-bond solid (TVBS) states are artificially generated by modulating edge shapes of the open clusters. We find that the energy per site of the HSS state is e0=E0/(NJ)=-1.41095, which is readily lower than that of the TVBS state (e0=-1.3912±0.0025). This agrees well with those of the cylindrical (e0=-1.4122) and periodic (e0=-1.4111) clusters where no assumption as to the ordering is posed. We further calculate the dimer-dimer correlation functions as well as the entanglement entropy of cylindrical clusters and conclude that a non-symmetry-breaking state is the ground state of the S=1 kagome Heisenberg model. Finally, we estimate the singlet-triplet energy gap: The HSS state has Δ/J=0.178±0.005, whereas the higher TVBS state has a larger one Δ/J=0.280.
  • Satoshi Nishimoto, Masaaki Nakamura
    PHYSICAL REVIEW B 92 14 140412(R)-1 - 5 2015年10月 [査読有り]
     研究論文(学術雑誌) 
    The S = 1 antiferromagnetic Heisenberg model on a kagome lattice is studied using the density-matrix renormalization-group method. To identify the ground state, we take four kinds of clusters into account; periodic, cylindrical, and two open ones. The hexagonal-singlet solid (HSS) and triangular valence-bond solid (TVBS) states are artificially generated by modulating edge shapes of the open clusters. We find that the energy per site of the HSS state is e(0) = E-0/(NJ) = -1.410 95, which is readily lower than that of the TVBS state (e(0) = -1.3912 +/- 0.0025). This agrees well with those of the cylindrical (e(0) = -1.4122) and periodic (e(0) = -1.4111) clusters where no assumption as to the ordering is posed. We further calculate the dimer-dimer correlation functions as well as the entanglement entropy of cylindrical clusters and conclude that a non-symmetry-breaking state is the ground state of the S = 1 kagome Heisenberg model. Finally, we estimate the singlet-triplet energy gap: The HSS state has Delta/J = 0.178 +/- 0.005, whereas the higher TVBS state has a larger one Delta/J = 0.280.
  • Zheng-Yuan Wang, Masaaki Nakamura
    J. Phys. Soc. Jpn. Conf. Proc. 4 013002-1 - 4 2015年01月 [査読有り]
     研究論文(国際会議プロシーディングス)
  • 汪 正元, 高吉 慎太郎, 中村 正明
    日本物理学会講演概要集 69 0 487 - 487 一般社団法人 日本物理学会 2014年 [査読有り]
  • 中村 正明, 汪 正元
    日本物理学会会誌 69 7 465 - 469 2014年 [査読有り]
     研究論文(その他学術会議資料等)
  • Zheng-Yuan Wang, Shunsuke C. Furuya, Masaaki Nakamura, Ryo Komakura
    PHYSICAL REVIEW B 88 22 224419-1 - 7 2013年12月 [査読有り]
     研究論文(学術雑誌) 
    We discuss spin-S antiferromagnetic Heisenberg chains with three-spin interactions, next-nearest-neighbor interactions, and bond alternation. First, we prove rigorously that there exist parameter regions of the exact dimerized ground state in this system. This is a generalization of the Majumdar-Ghosh model to arbitrary S. Next, we discuss the ground-state phase diagram of the models by introducing several effective field theories and the universality classes of the transitions are described by the level-2S SU(2) Wess-Zumino-Witten model and the Gaussian model. Finally, we determine the phase diagrams of S = 1 and S = 3/2 systems by using exact diagonalization and level spectroscopy.
  • Zheng-Yuan Wang, Masaaki Nakamura
    PHYSICAL REVIEW B 87 24 245119-1 - 9 2013年06月 [査読有り]
     研究論文(学術雑誌) 
    We introduce one-dimensional lattice models with exact matrix-product ground states describing the fractional quantum Hall (FQH) states in Laughlin series (given by filling factors nu = 1/q) on torus geometry. Surprisingly, the exactly solvable Hamiltonian has the same mathematical structure as that of the pseudopotential for the Laughlin wave function, and naturally derives the general properties of the Laughlin wave function such as the Z(2) properties of the FQH states and the fermion-boson relation. The obtained exact ground states have high overlaps with the Laughlin states and well describe their properties. Using the matrix product method, density functions and correlation functions are calculated analytically. Especially, obtained entanglement spectra reflect gapless edge states as was discussed by Li and Haldane.
  • Zheng-Yuan Wang, Shintaro Takayoshi, Masaaki Nakamura
    PHYSICAL REVIEW B 86 15 155104-1 - 7 2012年10月 [査読有り]
     研究論文(学術雑誌) 
    We discuss the relationship between fractional quantum Hall (FQH) states at filling factor nu = p/(2mp + 1) and quantum spin chains. This series corresponds to the Jain series nu = p/(2mp + 1) with m = 1 where the composite fermion picture is realized. We show that the FQH states with toroidal boundary conditions beyond the thin-torus limit can be mapped to effective quantum spin S = 1 chains with p spins in each unit cell. We calculate energy gaps and the correlation functions for both the FQH systems and the corresponding effective spin chains, using exact diagonalization and the infinite time-evolving block decimation (iTEBD) algorithm. We confirm that the mass gaps of these effective spin chains are decreased as p is increased which is similar to S = p integer Heisenberg chains. These results shed new light on a link between the hierarchy of FQH states and the Haldane conjecture for quantum spin chains.
  • 中村 正明
    Phys. Rev. Lett. 109 1 016401-1 - 5 2012年07月 [査読有り]
     研究論文(学術雑誌) 
    We introduce an exactly solvable fermion chain that describes a v = 1/3 fractional quantum Hall (FQH) state beyond the thin-torus limit. The ground state of our model is shown to be unique for each center-of-mass sector, and it has a matrix product representation that enables us to exactly calculate order parameters, correlation functions, and entanglement spectra. The ground state of our model shows striking similarities with the BCS wave functions and quantum spin-1 chains. Using the variational method with matrix product ansatz, we analytically calculate excitation gaps and vanishing of the compressibility expected in the FQH state. We also show that the above results can be related to a v = 1/2 bosonic FQH state.
  • Takeo Wakutsu, Masaaki Nakamura, Balazs Dora
    PHYSICAL REVIEW B 85 3 033403-1 - 4 2012年01月 [査読有り]
     研究論文(学術雑誌) 
    We study interlayer transport of multilayer graphenes in a magnetic field with various stacking structures (AB, ABC, and AA types) by calculating the Hall and longitudinal conductivities as functions of the Fermi energy. Their behavior depends strongly on the stacking structures and selection of the layers. The Hall conductivity between different layers is no longer quantized. Moreover, for AB stacking, the interlayer conductivity vanishes around zero energy with increasing layer separation, and shows negative values in particular cases. The fact that longitudinal interlayer conductivity is suppressed by a magnetic field indicates that this system can be applied as a switching device.
  • Masaaki Nakamura, Satoshi Nishimoto, Aroon O'Brien, Peter Fulde
    MODERN PHYSICS LETTERS B 25 12-13 947 - 953 2011年05月 [査読有り]
     研究論文(学術雑誌) 
    We discuss the metal-insulator transition of the spinless farm ion model with nearest-neighbor repulsion on the Kagome lattice at 1/3- and 2/3-filling. The system is analyzed by using exact diagonalization, the density-matrix renormalization group methods and the random phase approximation. In the strong-coupling region, the system is described by ring exchange processes. In the intermediate-coupling regime, we find that the qualitative properties of the metal-insulator transition at 1/3- and 2/3-filling are totally different reflecting the difference in the band structure near the Fermi level.
  • 汪 正元, 中村 正明, Bergholtz Emil Johansson, 高吉 慎太郎
    日本物理学会講演概要集 66 0 238 - 238 一般社団法人 日本物理学会 2011年 [査読有り]
  • Emil J. Bergholtz, Masaaki Nakamura, Juha Suorsa
    PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES 43 3 755 - 760 2011年01月 [査読有り]
     研究論文(学術雑誌) 
    Fractional quantum Hall (FQH) states are topologically ordered which indicates that their essential properties are insensitive to smooth deformations of the manifold on which they are studied. Their microscopic Hamiltonian description, however, strongly depends on geometrical details. Recent work has shown how this dependence can be exploited to generate effective models that are both interesting in their own right and also provide further insight into the quantum Hall system. We review and expand on recent efforts to understand the FQH system close to the solvable thin-torus limit in terms of effective spin chains. In particular, we clarify how the difference between the bosonic and fermionic FQH states, which is not apparent in the thin-torus limit, can be seen at this level. Additionally, we discuss the relation of the Haldane-Shastry chain to the so-called QH circle limit and comment on its significance to recent entanglement studies. (C) 2010 Elsevier B.V. All rights reserved.
  • Masaaki Nakamura, Zheng-Yuan Wang, Emil J. Bergholtz
    INTERNATIONAL SYMPOSIUM: NANOSCIENCE AND QUANTUM PHYSICS 2011 (NANOPHYS'11) 302 012020-1 - 8 2011年 [査読有り]
     研究論文(国際会議プロシーディングス) 
    We discuss the relationship between the fractional quantum Hall effect in the vicinity of the thin-torus, Tao-Thouless (TT), limit and quantum spin chains. We argue that the energetics of fractional quantum Hall states in Jain sequence at filling fraction v = p/(2p + 1) (and v = 1 p/(2p + 1)) in the lowest Landau level is captured by S = 1 spin chains with p spins in the unit cell. These spin chains naturally arise at sub-leading order in e(-2 pi 2)/L-1(2) which serves as an expansion parameter away from the TT limit (L-1 -> 0). We also corroborate earlier results on the smooth Fermi surface deformation of the gapless state at; v = 1/2, interpolating between a state described by a critical S = 1/2 chain and the bulk.
  • Satoshi Nishimoto, Masaaki Nakamura, Aroon O'Brien, Peter Fulde
    PHYSICAL REVIEW LETTERS 104 19 196401-1 - 4 2010年05月 [査読有り]
     研究論文(学術雑誌) 
    We discuss the metal-insulator transition of the spinless fermion model on a kagome lattice at 1/3 filling. The system is analyzed by using exact diagonalization, density-matrix renormalization group methods, and random-phase approximation. In the strong-coupling region, the charge-ordered ground state is consistent with the predictions of an effective model, i.e., plaquette order. We find that the qualitative properties of the metal-insulator transition are totally different depending on the sign of the hopping matrix elements, reflecting the difference in the band structure near the Fermi level.
  • Masaaki Nakamura, Emil J. Bergholtz, Juha Suorsa
    PHYSICAL REVIEW B 81 16 165102-1 - 8 2010年04月 [査読有り]
     研究論文(学術雑誌) 
    We study a strong coupling expansion of the nu = 1/3 fractional quantum Hall state away from the Tao-Thouless limit and show that the leading quantum fluctuations lead to an effective spin-1 Hamiltonian that lacks parity symmetry. By analyzing the energetics, discrete symmetries of low-lying excitations, and string order parameters, we demonstrate that the nu = 1/3 fractional quantum Hall state is adiabatically connected to both Haldane and large-D phases and is characterized by a string order parameter which is dual to the ordinary one. This result indicates a close relation between (a generalized form of) the Haldane conjecture for spin chains and the fractional quantum Hall effect.
  • Masaaki Nakamura, Eduardo V. Castro, Balazas Dora
    PHYSICAL REVIEW LETTERS 103 26 266804-1 - 4 2009年12月 [査読有り]
     研究論文(学術雑誌) 
    Physical properties reflecting the valley asymmetry of Landau levels in a biased bilayer graphene under a magnetic field are discussed. Within the 4-band continuum model with a Hartree-corrected self-consistent gap and finite damping factor we predict the appearance of anomalous steps in quantized Hall conductivity due to the degeneracy lifting of Landau levels. Moreover, the valley symmetry breaking effect appears as a nonsemiclassical de Haas-van Alphen effect where the reduction of the oscillation period to half cannot be accounted for through quasiclassical quantization of the orbits in reciprocal space.
  • Masaaki Nakamura, Lila Hirasawa
    25TH INTERNATIONAL CONFERENCE ON LOW TEMPERATURE PHYSICS (LT25), PART 2 150 022064-1 - 4 2009年 [査読有り]
     研究論文(国際会議プロシーディングス) 
    We discuss Hall effect of multilayer graphenes with several stacking structures (Bernal, rhombohedral and simple hexagonal) in strong- and weak-magnetic field regimes. For bilayer systems in strong-magnetic field region, we observed crossover of integer quantum Hall effect from two independent monolayer type system to strongly coupled bilayer systems by changing the ratio of interlayer hopping energy and the Fermi energy. In weak-magnetic field regime of few layer systems, Hall conductivity shows plateaux as functions of Fermi energy which reflects difference of stacking structures.
  • Balazs Dora, Klaus Ziegler, Peter Thalmeier, Masaaki Nakamura
    PHYSICAL REVIEW LETTERS 102 3 036803-1 - 4 2009年01月 [査読有り]
     研究論文(学術雑誌) 
    We investigate the relation between the canonical model of quantum optics, the Jaynes-Cummings Hamiltonian and Dirac fermions in quantizing magnetic field. We demonstrate that Rabi oscillations are observable in the optical response of graphene, providing us with a transparent picture about the structure of optical transitions. While the longitudinal conductivity reveals chaotic Rabi oscillations, the Hall component measures coherent ones. This opens up the possibility of investigating a microscopic model of a few quantum objects in a macroscopic experiment with tunable parameters.
  • Masaaki Nakamura, Lila Hirasawa, Ken-Ichiro Imura
    PHYSICAL REVIEW B 78 3 033403-1 - 4 2008年07月 [査読有り]
     研究論文(学術雑誌) 
    We discuss the quantum Hall effect of bilayer graphene with finite gate voltage where the Fermi energy exceeds the interlayer hopping energy. We calculated magnetic susceptibility, and diagonal and off-diagonal conductivities in finite-magnetic-field formalism. We also observed crossover of integer quantum Hall effect from two independent monolayer type systems to a strongly coupled bilayer system by changing the ratio of interlayer hopping energy and the Fermi energy. We also discuss the case of multilayer systems with Bernal stacking.
  • Masaaki Nakamura, Lila Hirasawa
    Physical Review B - Condensed Matter and Materials Physics 77 4 2008年01月 [査読有り]
     研究論文(学術雑誌) 
    We discuss electric transport and orbital magnetism of multilayer graphenes in a weak-magnetic field using the matrix decomposition technique. At zero temperature, the minimum conductivity is given by that of the monolayer system multiplied by the layer number N, independent of the interlayer hopping t. When the interlayer hopping satisfies the condition t τ with τ being collision time of impurity scattering, [N 2] kinks and [N 2] +1 plateaux appear in the Fermi-energy (gate voltage) dependence of the conductivity and the Hall conductivity, respectively. These behaviors are interpreted as multiband effects. We also found that the Hall conductivity and the magnetic susceptibility take minimum value as a function of temperature, for certain value of the gate voltage. This behavior is explained by Fermi-energy dependence of these functions at zero temperature. © 2008 The American Physical Society.
  • Masaaki Nakamura, Lila Hirasawa
    PHYSICAL REVIEW B 77 4 045429-1 - 10 2008年01月 [査読有り]
     研究論文(学術雑誌) 
    We discuss electric transport and orbital magnetism of multilayer graphenes in a weak-magnetic field using the matrix decomposition technique. At zero temperature, the minimum conductivity is given by that of the monolayer system multiplied by the layer number N, independent of the interlayer hopping t. When the interlayer hopping satisfies the condition t > h/tau with tau being collision time of impurity scattering, [N/2] kinks and [N/2]+1 plateaux appear in the Fermi-energy (gate voltage) dependence of the conductivity and the Hall conductivity, respectively. These behaviors are interpreted as multiband effects. We also found that the Hall conductivity and the magnetic susceptibility take minimum value as a function of temperature, for certain value of the gate voltage. This behavior is explained by Fermi-energy dependence of these functions at zero temperature.
  • Masaaki Nakamura
    PHYSICAL REVIEW B 76 11 113301-1 - 4 2007年09月 [査読有り]
     研究論文(学術雑誌) 
    We discuss the orbital magnetism and the Hall effect in a weak magnetic field in two-dimensional Dirac fermion systems with an energy gap. This model is related to the graphene sheet, zero-gap organic conductors, and the d-density-wave state of cuprates. We found strong diamagnetism and anomalous Hall conductivity even in gapped systems. We also discuss the relation between results of the weak-magnetic-field formalism and those in a finite magnetic field with Landau quantization.
  • Masaaki Nakamura, Kazuyoshi Yoshimi, Hatsumi Mori
    JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS 310 2 1099 - 1101 2007年03月 [査読有り]
     研究論文(学術雑誌) 
    We study superconductivity mediated by the charge fluctuation in two-dimensional organic conductor beta-(meso-DMBEDT-TTF)(2)PF6. We consider the extended Hubbard model on a weakly dimerized lattice, and solve the Eliashberg equations based on the random phase approximation. We found reentrant behavior of the checkerboard-type charge-ordered phase in the phase diagram, and the triplet superconductivity due to the charge fluctuation in the neighboring region. This results well agree with the experimental fact. (c) 2006 Elsevier B.V. All rights reserved.
  • Hiromi Otsuka, Masaaki Nakamura
    JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS 310 2 1119 - 1121 2007年03月 [査読有り]
     研究論文(学術雑誌) 
    Two electron systems in one dimension, the quarter-filled extended Hubbard model with the alternating transfer integral and the half-filled ionic Hubbard model, are investigated. In both cases, their charge parts are expected to show the Ising criticality. We numerically determine the phase diagrams, and perform the finite-size scaling analysis of an excitation gap to show the evidence. Furthermore, we give the relationship between the twist operator and the Ising order parameter in a certain limit. (c) 2006 Elsevier B.V. All rights reserved.
  • Kazuyoshi Yoshimi, Masaaki Nakamura, Hatsumi Mori
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 76 2 024706-1 - 8 2007年02月 [査読有り]
     研究論文(学術雑誌) 
    We study theoretically competition between the charge ordering and the superconductivity in the two-dimensional organic conductor beta-(meso-DMBEDT-TTF)(2)PF6. We analyze the extended Hubbard model on a weakly-dimerized lattice based on the random phase approximation and Eliashberg equations. We found the reentrant behavior of the checkerbord-type charge-ordered phase in the phase diagram, and the triplet superconductivity due to the charge fluctuation in the neighboring region. In low temperatures, the singlet superconductivity also appears due to the enhancement of the spin fluctuation.
  • S Konabe, T Nikuni, M Nakamura
    PHYSICAL REVIEW A 73 3 033621-1 - 12 2006年03月 [査読有り]
     研究論文(学術雑誌) 
    We study single-particle excitations of a Bose gas in an optical lattice in the Mott-insulator phase. The characteristic feature of the single-particle spectrum in the Mott-insulator phase is the existence of an energy gap between the particle and hole excitations. We show that the single-particle excitation energies and associated energy gap in the Mott-insulator phase can be directly probed by an output-coupling experiment. We apply the general expression for the output current derived by Luxat and Griffin, which is given in terms of the single-particle Green's functions of a trapped Bose gas, to the Mott-insulator phase using the Bose-Hubbard model. The energy spectrum of the momentum-resolved output current exhibits two characteristic peaks corresponding to the particle and hole excitations, and thus it can be used to detect the transition point from the Mott insulator to superfluid phase where the energy gap disappears.
  • S. Konabe, T. Nikuni, M. Nakamura
    Physical Review A - Atomic, Molecular, and Optical Physics 73 3 2006年 [査読有り]
     研究論文(学術雑誌) 
    We study single-particle excitations of a Bose gas in an optical lattice in the Mott-insulator phase. The characteristic feature of the single-particle spectrum in the Mott-insulator phase is the existence of an energy gap between the particle and hole excitations. We show that the single-particle excitation energies and associated energy gap in the Mott-insulator phase can be directly probed by an output-coupling experiment. We apply the general expression for the output current derived by Luxat and Griffin, which is given in terms of the single-particle Green's functions of a trapped Bose gas, to the Mott-insulator phase using the Bose-Hubbard model. The energy spectrum of the momentum-resolved output current exhibits two characteristic peaks corresponding to the particle and hole excitations, and thus it can be used to detect the transition point from the Mott insulator to superfluid phase where the energy gap disappears. © 2006 The American Physical Society.
  • M Nakamura, T Okano, K Itoh
    PHYSICAL REVIEW B 72 11 115121-1 - 8 2005年09月 [査読有り]
     研究論文(学術雑誌) 
    We discuss the exact bond-ordered ground states of the one-dimensional half-filled generalized Hubbard model including three- and four-body terms, by decomposing the Hamiltonian into positive semidefinite parts. The obtained exact ground states are interpreted as Neel ordered states on the bond-located electrons. We determine parameter regions of the exact ground states. We also calculate elementary excitation energies as variational approach based on the matrix-product formalism.
  • H Otsuka, M Nakamura
    PHYSICAL REVIEW B 71 15 155105-1 - 7 2005年04月 [査読有り]
     研究論文(学術雑誌) 
    We investigate the ground-state phase diagram of the one-dimensional half-filled Hubbard model with an alternating potential-a model for the charge-transfer organic materials and the ferroelectric perovskites. We numerically determine the global phase diagram of this model using the level-crossing and the phenomenological renormalization-group methods based on the exact diagonalization calculations. Our results support the mechanism of the double phase transitions between Mott and band insulators pointed out by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014 (1999)]: We confirm the existence of the spontaneously dimerized phase as an intermediate state. Further we provide numerical evidence to check the criticalities on the phase boundaries. Especially, we perform the finite-size-scaling analysis of the excitation gap to show the two-dimensional Ising transition in the charge part. On the other hand, we confirm that the dimerized phase survives in the strong-coupling limit, which is one of the resultants of competition between the ionicity and correlation effects.
  • H Otsuka, M Nakamura
    PHYSICA B-CONDENSED MATTER 359 1430 - 1432 2005年04月 [査読有り]
     研究論文(学術雑誌) 
    We study two one-dimensional electron systems, i.e., the quarter-filled extended Hubbard model with the alternating transfer integral and the half-filled ionic Hubbard model. In both cases, their charge parts are expected to show the two-dimensional Ising criticality as a resultant of two competing relevant perturbations on the Tomonaga-Luttinger liquid, and its description is given by the double-frequency sine-Gordon theory. Analyzing the excitation spectra of finite-size systems, we numerically determine the ground-state phase diagrams and check the theoretical predictions. (c) 2005 Elsevier B.V. All rights reserved.
  • Masaaki Nakamura, Kazuhito Itoh
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 74 234 - 237 2005年 [査読有り]
     研究論文(学術雑誌) 
    We show the existance of the exact plaquette-ordered ground states of the Hubbard model including site-off-diagonal interactions in arbitrary dimensions, by decomposing the Hamiltonian as sum of products of projection operators for each spin sector. The obtatined exact ground states are interpreted as Neel ordered states on the dual lattices. We demonstrate this idea in the one-dimensional chain and higher-dimensional lattices such as the Kagome lattice, and determine parameter regions of the exact ground states.
  • Hiromi Otsuka, Masaaki Nakamura
    Physical Review B - Condensed Matter and Materials Physics 70 7 1 - 73105 2004年08月 [査読有り]
     研究論文(学術雑誌) 
    We study the one-dimensional quarter-filled extended Hubbard model with an alternating transfer integral. In the strong-dimerization limit the charge part is described by the quantum Ising model which shows the two-dimensional Ising criticality at the self-dual point, and it is naturally connected to the double-frequency sine-Gordon theory in the weak dimerization. Treating low-lying excitations in finite-size systems, we numerically determine a phase boundary between two types of 4kF density-wave states and clarify the ground-state phase diagram. Further, we refer to its relevances to the charge-ordered phase observed in the charge-transfer organic salts.
  • H Otsuka, M Nakamura
    PHYSICAL REVIEW B 70 7 073105-1 - 4 2004年08月 [査読有り]
     研究論文(学術雑誌) 
    We study the one-dimensional quarter-filled extended Hubbard model with an alternating transfer integral. In the strong-dimerization limit the charge part is described by the quantum Ising model which shows the two-dimensional Ising criticality at the self-dual point, and it is naturally connected to the double-frequency sine-Gordon theory in the weak dimerization. Treating low-lying excitations in finite-size systems, we numerically determine a phase boundary between two types of 4k(F) density-wave states and clarify the ground-state phase diagram. Further, we refer to its relevances to the charge-ordered phase observed in the charge-transfer organic salts.
  • NAKAMURA Masaaki
    Journal of Magnetism and Magnetic Materials 272-276 914 - 915 2004年05月 [査読有り]
     研究論文(学術雑誌)
  • T Momoi, T Hikihara, M Nakamura, Hu, X
    PHYSICAL REVIEW B 67 17 2003年05月 [査読有り]
     研究論文(学術雑誌) 
    We show that scalar chiral order can be induced by four-spin exchanges in the two-leg spin ladder, using the spin-chirality duality transformation and matrix-product ansatz. Scalar-chiral-ordered states are found to be exact ground states in a family of spin ladder models. In this scalar chiral phase, there is a finite energy gap above the doubly degenerate ground states and a Z(2)xZ(2)xZ(2) symmetry is fully broken. It is also shown that the SU(4)-symmetric model, which is self-dual under the duality transformation, is on a multicritical point surrounded by the staggered dimer phase, the staggered scalar chiral phase, and the gapless phase.
  • M Nakamura
    PHYSICA B-CONDENSED MATTER 329 1000 - 1001 2003年05月 [査読有り]
     研究論文(学術雑誌) 
    We discuss relation between three different methods to identify topologically distinct short-range valence-bond ground states in spin-1/2 two-leg ladders: the string order parameters, the level-crossing method, and the ground-state 2 expectation value of the twist operator. For this purpose we reexamine a phase transition in the frustrated spin ladder. We propose a proper bosonization of the string order parameters. Then, these three methods are shown to be equivalent reflecting the Z(2) x Z(2) symmetry breaking of the order and the disorder fields of the two-dimensional Ising model. (C) 2003 Elsevier Science B.V. All rights reserved.
  • M Matsumoto, S Todo, M Nakamura, C Yasuda, H Takayama
    PHYSICA B-CONDENSED MATTER 329 1010 - 1011 2003年05月 [査読有り]
     研究論文(学術雑誌) 
    We have proposed the plaquette-singlet solid (PSS) ground state for the spin-1 antiferromagnetic Heisenberg two-leg ladder. Based on the PSS picture, we discuss, the correspondence of the PSS state to the valence-bond solid (VBS) state of the ground state of spin-2 chain by introducing an appropriate composite spin picture. When the bond alternation is introduced, there occur quantum phase transitions and each phase can be identified with that in the dimerized spin-2 chain. Furthermore, we argue that the VBS picture of spin-2S chain can be applied to the ground state of spin-S two-leg ladder. (C) 2003 Elsevier Science B.V. All rights reserved.
  • M Nakamura, T Yamamoto, K Ide
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 72 5 1022 - 1025 2003年05月 [査読有り]
     研究論文(学術雑誌) 
    We study phase transition between two topologically different gapped states in the spin-1/2 bond-alternating two-leg Heisenberg ladder by investigating string order parameters and the level-crossing method based on the exact diagonalization. We determine the phase diagram on the plane of the bond-alternation delta and the rung-leg coupling ratio J(perpendicular to)/J, and conclude that the boundary is given as J(perpendicular to)/J proportional to delta(2/3) in the weak coupling region J(perpendicular to)/J, delta much less than 1.
  • Momoi, T, Hikihara, T, Nakamura, M, Hu, X
    Physical Review B 67 174410-1 - 8 2003年 [査読有り]
     研究論文(学術雑誌)
  • M Nakamura, S Todo
    PHYSICAL REVIEW LETTERS 89 7 077204  2002年08月 [査読有り]
     研究論文(学術雑誌) 
    We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the number of valence bonds (broken valence bonds) at the boundary for periodic (open) systems. This allows us to determine the phase transition point in between different VBS states. We demonstrate this theory in the successive dimerization transitions of the bond-alternating Heisenberg chains, using the quantum Monte Carlo method.
  • M Nakamura, J Voit
    PHYSICAL REVIEW B 65 15 153110  2002年04月 [査読有り]
     研究論文(学術雑誌) 
    In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twist operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values z(L)((q)) measure the overlap between the q-fold degenerate ground state and an excited state. Insulators are characterized by z(infinity)not equal0, and different states are distinguished by the sign of z(L). We identify z(L) with ground-state expectation values of vertex operators in the sine-Gordon model. This allows an accurate detection of quantum phase transitions in the universality classes of the Gaussian and the SU(2)(1) Wess-Zumino-Novikov-Witten models. We apply this theory to the half-filled extended Hubbard model and obtain agreement with the level-crossing method.
  • M Nakamura, S Todo
    PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT 145 145 217 - 220 2002年 [査読有り]
     研究論文(学術雑誌) 
    We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin systems, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the configuration of the valence bonds. This allows us to determine the phase transition point in between different VBS states accurately. We demonstrate this theory in the bond-alternating Heisenberg chain and in the frustrated spin ladder.
  • M Nakamura, K Itoh
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 70 12 3606 - 3612 2001年12月 [査読有り]
     研究論文(学術雑誌) 
    Phase diagram of the one-dimensional extended Hubbard model with a nearest neighbor interaction V and site-off-diagonal (bond-charge X and bond-bond W) interactions at half-filling is obtained analytically and numerically. For the numerical analysis, we used the level-crossing approach which has been applied to the W = 0 case [Phys. Rev. B 61 (2001) 16377]. Similarly to the X term, the W term enhances bond-charge-density-wave (BCDW) and bond-spin-density-wave (BSDW) phases for W < 0 and W > 0 cases, respectively. In addition we showed that an exact ground state corresponding to a BSDW state, and an eta -pairing ground state appear in this model.
  • K Itoh, M Nakamura, N Muramoto
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 70 5 1202 - 1205 2001年05月 [査読有り]
     研究論文(学術雑誌) 
    We Show the existence of all exact ground state in a parameter regime of a one-dimensional half-filled extended Hubbard model with site-off-diagonal interactions. In this ground state, the bond-located spin correlation exhibits a long-range order. In the case when the spin space is SU(2) symmetric, this ground state degenerates with higher spin states including a fully ferromagnetic state. We also discuss the relation between the exact bond-ordered ground state and the critical bond-spin-density-wave phase.
  • M Nakamura
    PHYSICAL REVIEW B 61 24 16377 - 16392 2000年06月 [査読有り]
     研究論文(学術雑誌) 
    Phase diagrams of the one-dimensional extended Hubbard model (including nearest-neighbor interaction V) at half- and quarter-filling are studied by observing level crossings of excitation spectra using the exact diagonalization. This method is based on the Tomonaga-Luttinger liquid theory including logarithmic corrections which stem from the renormalization of the Umklapp- and the backward-scattering effects. Using this approach, the phase boundaries are determined with high accuracy, and then the structure of the phase diagram is clarified. At half-filling, the phase diagram consists of two Berezinskii-Kosterlitz-Thouless (BKT) transition lines and one Gaussian transition line in the charge sector, and one spin-gap transition line. This structure reflects the U(1) x SU(2) symmetry of the electron system. Near the U = 2V line, the Gaussian and the spin-gap transitions take place independently from the weak- to the intermediate-coupling region, but these two transition lines are coupled in the strong-coupling region. This result demonstrates existence of a tricritical point and a bond-charge-density-wave (BCDW) phase between charge- and spin-density-wave (CDW, SDW) phases. To clarify this mechanism of the transition, we also investigate effect of a correlated hopping term, which plays a role to enlarge BCDW and bond-spin-density-wave (BSDW) phases. At quarter-filling, a similar crossover phenomenon also takes place in the large-V region involving spin-gap and BKT-type metal-insulator transitions.
  • M Nakamura
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 68 10 3123 - 3126 1999年10月 [査読有り]
     研究論文(学術雑誌) 
    The phase transition between charge- and spin-density-wave (CDW, SDW) phases is studied in the one-dimensional extended Hubbard model at half-filling. We discuss whether the transition can be described by Gaussian and spin-gap transitions under charge-spin separation, or by the direct CDW-SDW transition. These phase boundaries are determined by level crossings of excitation spectra which are identified according to discrete symmetries of wave functions. We conclude that the Gaussian and spin-gap transitions take place separately from the weak- to intermediate-coupling region, and a bond-order-wave phase exists between the CDW and the SDW states. Our results Are also consistent with those of the strong-coupling theory and of the direct evaluation of the CDW order parameters.
  • M Nakamura, A Kitazawa, K Nomura
    PHYSICAL REVIEW B 60 11 7850 - 7862 1999年09月 [査読有り]
     研究論文(学術雑誌) 
    We give details of the analysis of critical properties of spin-gap phases in one-dimensional lattice electron models. In Tomonaga-Luttinger (TL) liquid theory, the spin-gap instability occurs when the backward scattering changes from repulsive to attractive. This transition point is, shown to be equivalent to that of the level-crossing of the singlet and triplet excitation spectra, using the c=1 conformal field theory and the renormalization group. Based on this notion, the transition point between the TL liquid and the spin-gap phases can be determined with high-accuracy, from the numerical data of finite-size clusters. We also discuss the boundary conditions and discrete symmetries to extract these excitation spectra. This technique is applied to the extended Hubbard model, the t-J model, and the t-J-J' model, and their phase diagrams are obtained. We also discuss the relation between our results and analytical solutions in weak-coupling and low-density limits.
  • M Nakamura
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 67 3 717 - 720 1998年03月 [査読有り]
     
    The spin-gap phase of the one-dimensional t-J-J' model is studied by the level-crossing of the singlet and the triplet excitation spectra. The phase boundary obtained between the Tomonaga-Luttinger and the spin-gap phases is remarkably consistent with the analytical results at the J, J' --> 0 and the low-density limits discussed by Ogata et al. The spin-gap phase has a single domain in the phase diagram even if the spin gap opens at half-filling. The phase boundary coincides with the K-p = 1 line where the Tomonaga-Luttinger liquid behaves as free electrons, in the low-density region. The relation between our method and the solution of the two-electron problem is also discussed.
  • M Nakamura, K Nomura
    PHYSICAL REVIEW B 56 20 12840 - 12846 1997年11月 [査読有り]
     研究論文(学術雑誌) 
    Asymptotic behavior of the Tomonaga-Luttinger liquid in the vicinity of the phase-separated region is investigated in the one-dimensional t-J model to study the universal property of the c = 1 conformal field theory with U(1) symmetry near the K --> infinity instability. By analogy to the spinless fermion, we argue that the compressibility behaves as kappa proportional to (J(c) - J)(-1), and that the Drude weight is constant and changes to zero discontinuously at the phase boundary. This speculation is confirmed by analyzing the finite-size effect from the result of the exact diagonalization.
  • M Nakamura, K Nomura, A Kitazawa
    PHYSICAL REVIEW LETTERS 79 17 3214 - 3217 1997年10月 [査読有り]
     研究論文(学術雑誌) 
    We study the spin-gap phase in the one-dimensional t-J model, assuming that it is caused by the backward scattering process. Based on the renormalization group analysis and symmetry, we can determine the transition point between the Tomonaga-Luttinger liquid and the spin-gap phases, by the level crossing of the singlet and the triplet excitations. In contrast to the previous works, the obtained spin-gap region is unexpectedly large. We also determine that the universality class of the transition belongs to the k = 1 SU(2) Wess-Zumino-Witten model.

講演・口頭発表等

  • 偏極演算子の高次元化とトポロジカル秩序変数
    中村正明, 西本理, 三澤貴宏
    日本物理学会 2020年09月
  • ひねり演算子と変分波動関数を用いた電子系のトポロジカル相転移の解析
    中村, 正明,三澤, 貴宏
    日本物理学会 2020年03月
  • Exact Plaquette-Ordered Ground States with Exact Corner States of the Generalized Hubbard Model in Corner Sharing Lattices
    M. Nakamura
    SCES2019 2019年09月
  • 一般化ハバード模型における厳密なプラケット秩序状態とコーナー状態
    中村正明
    日本物理学会 2019年09月 口頭発表(一般)
  • Exact Plaquette-Ordered Ground States with Exact Corner States of the Generalized Hubbard Model in Corner Sharing Lattices  [通常講演]
    中村 正明
    FSP2019 (FRONTIERS OF STATISTICAL PHYSICS) 2019年06月 ポスター発表
  • 量子スピン系における偏極演算子 を用いたトポロジカル情報の抽出  [通常講演]
    中村 正明
    2018年11月 口頭発表(一般) 基研研究会「スピン系物理の最前線」
  • 量子スピン系における偏極演算子を用いたトポロジカル情報の増幅と抽出  [通常講演]
    中村 正明
    2018年09月 口頭発表(一般) 物性研研究会「量子情報・物性の新潮流」
  • 朝永・Luttinger液体における偏極演算子によるトポロジカル情報の増幅と抽出  [通常講演]
    中村 正明
    2018年08月 ポスター発表 同志社大学(京田辺キャンパス) 日本物理学会 2018年秋季大会
  • 1次元量子系における偏極演算子によるトポロジカル数の検出  [通常講演]
    中村 正明
    日本物理学会 2018年次大会 2018年03月 口頭発表(一般)
  • カゴメ格子拡張Hubbard模型におけるプラケット厳密基底状態とその数値的検証  [通常講演]
    中村 正明, 西本 理
    日本物理学会 2017年秋季大会 2017年09月 口頭発表(一般)
  • トポロジカル絶縁体における磁気応答  [通常講演]
    土田浩平, 坂上和海, 中村正明
    2017年03月 ポスター発表
  • トポロジカル絶縁体における動的スピン磁化率  [通常講演]
    中村 正明
    2017年03月 口頭発表(一般)
  • Detection of topological states in two-dimensional Dirac systems by the dynamic spin susceptibility  [通常講演]
    中村 正明
    Theory of Correlated Topological Materials (TCTM2017) ISSP University of Tokyo 2017年02月 口頭発表(一般)
  • 動的スピン帯磁率によるトポロジカル状態の検出  [通常講演]
    中村 正明
    平成28年度後期客員所員講演会、東京大学物性研究所 2016年10月 口頭発表(招待・特別)
  • Detection of topological states in two-dimensional Dirac systems by the dynamic spin susceptibility  [通常講演]
    中村 正明
    YITP workshop, bulk-edge correspondence 2016 (BEC2016) 2016年09月 ポスター発表
  • ランダウ準位が交差したν=1/2分数量子ホール状態のThin-Torus極限  [通常講演]
    汪 正元, 中村 正明
    日本物理学会 2016年09月 口頭発表(一般)
  • 動的スピン磁化率を用いたトポロジカル絶縁体の検出法とその応用  [通常講演]
    中村 正明
    日本物理学会 2016年09月 口頭発表(一般)
  • Detection of topological states in two-dimensional Dirac systems by the dynamic spin susceptibility  [通常講演]
    中村 正明
    APS March Meeting 2016, Baltimore, MD, USA 2016年03月 口頭発表(基調)
  • Detection of topological states in two-dimensional Dirac systems by the dynamic spin susceptibility  [通常講演]
    中村 正明
    Topological Phenomena in Novel Quantum Matter: Laboratory Realization of Relativistic Fermions and Spin Liquids (topmat16) 2016年03月 ポスター発表
  • 2次元Dirac系における動的スピン帯磁率によるトポロジカル状態の検出  [通常講演]
    中村 正明
    日本物理学会 2015年09月 口頭発表(一般)

MISC

共同研究・競争的資金等の研究課題

  • 強相関量子系に対するトポロジーおよび情報幾何的側面からの理論的研究
    文部科学省:科学研究費補助金 基盤研究C
    研究期間 : 2020年04月 -2024年03月 
    代表者 : 中村正明
  • 新奇なトポロジカル物理現象の探索とその検出法に関する理論的研究
    文部科学省:科学研究費補助金 基盤研究C
    研究期間 : 2017年04月 -2020年03月 
    代表者 : 中村 正明
  • 2次元量子系におけるトポロジカルな秩序と新奇な輸送現象
    文部科学省:科学研究費補助金 基盤研究C
    研究期間 : 2011年04月 -2014年03月 
    代表者 : 中村 正明
  • 低次元強相関系における新奇な基底状態と有限温度の輸送現象
    文部科学省:科学研究費補助金 若手研究B
    研究期間 : 2004年04月 -2006年03月 
    代表者 : 中村 正明
  • ひねり演算子を用いた低次元強相関系の統計力学的研究
    文部科学省:科学研究費補助金 若手研究B
    研究期間 : 2002年04月 -2004年03月 
    代表者 : 中村 正明

担当経験のある科目

  • 量子力学演習Ⅱ愛媛大学
  • 量子力学Ⅱ愛媛大学
  • 量子力学演習Ⅰ愛媛大学
  • 量子力学Ⅰ愛媛大学
  • 相対性理論愛媛大学
  • 量子力学特論愛媛大学
  • 量子力学III愛媛大学
  • 物理数学II愛媛大学
  • 物理数学演習愛媛大学
  • 物理数学I愛媛大学
  • 新入生セミナーA愛媛大学
  • 量子力学演習II愛媛大学
  • 物理学II愛媛大学
  • 高校物理慶応義塾大学志木高等学校
  • コンピュータ2東京理科大学
  • 量子力学演習東京理科大学
  • 熱統計力学演習東京理科大学
  • 物理数学2東京理科大学
  • 統計力学演習東京理科大学
  • 多体系の量子力学東京工業大学
  • 現代物理学序論愛媛大学

愛媛大学教員活動実績

教育活動(B)

担当授業科目(B01)

  • 2019, 前期, 学部, 相対性理論
  • 2019, 前期, 学部, 量子力学Ⅰ
  • 2019, 前期, 学部, 量子力学演習I
  • 2019, 前期, 学部, 量子力学Ⅲ
  • 2019, 前期, 学部, 卒業研究Ⅰ
  • 2019, 前期, 学部, 卒業研究Ⅱ
  • 2019, 前期, 修士, 量子力学特論


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