物性理論専攻大学院1年生が習得すべき理論ミニマム

(C)T. Saso, 1996,2006 一度は読んでおくべき,基本的な原論文を記載しています。もちろん,これがすべてではありません。明らかに,強相関電子系に偏っています。

(現在(永遠に)作成中,未記入の項目が多くてすみません。)
(minimumというのは,もちろんjokeです。(^_^))

多粒子系に対する場の理論的手法

 これについては,「物性理論参考書」のページを見てください。

・Hartree-Fock近似
・第2量子化法
・Green関数の性質(絶対0度)
  Wickの定理,摂動展開,結合クラスター定理,スペクトル表示,準粒子の性質
  Dyson方程式
・Green関数の性質(有限温度)
  Bloch-de Dominicisの定理,摂動展開,スペクトル表示,解析接続

線形応答理論(久保公式)と温度グリーン関数

・久保公式と揺動散逸定理
  R. Kubo: J. Phys. Soc. Jpn. 12 (1957) 570
  D.N. Zubarev: Sov. Phys.-Uspekhi 3 (1960) 320
・自由電子系の誘電関数,動的帯磁率などの計算法

Grassmann数と汎関数積分

  J. Negele and H. Orland, "Quantum Many-Particle Systems" (Addison-Weyley, 1987)

Bogoliubovの不等式とMermin-Wagnerの定理

  N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133-1136 (1966)

一様な電子ガス

・RPA
  D. Bohm and D. Pines, Phys. Rev. 92 (1953) 609
  M. Gell-Mann and K.A. Brueckner: Phys. Rev. 106 (1957) 354
  H. Ehrenreich and M.H. Cohen, Phys. Rev. 115 (1959) 786
・遮蔽

Kohn-Sham理論

  W. Kohn and L. J. Sham,Phys. Rev. 140, A1133-A1138 (1965)
  L. J. Sham and W. Kohn Phys. Rev. 145, 561-567 (1966)

LandauのFermi液体論

  L. Landau: Sov. Phys. JETP 3 (1957) 920; ibid 5 (1957) 101; ibid 8 (1959) 70

LuttingerのFermi液体論

  J. M. Luttinger, Analytic Properties of Single-Particle Propagators for Many-Fermion Systems, Phys. Rev. 121, 942-949 (1961)
  J. M. Luttinger Fermi Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions, Phys. Rev. 119, 1153-1163 (1960)
  J. M. Luttinger and J. C. Ward, Ground-State Energy of a Many-Fermion System. II Phys. Rev. 118, 1417-1427 (1960)
  W. Kohn and J. M. Luttinger, Ground-State Energy of a Many-Fermion System Phys. Rev. 118, 41-45 (1960)Luttinger

BCS理論

  J. Bardeen, L. Cooper and J. R. Schrieffer: Phys. Rev. 108 (1957) 1175
  L.P. Gorkov: Sov. Phys. JETP 9 (1959) 1346
  A.A. Abrikosov and L.P. Gorkov: Sov. Phys. JETP 12 (1961) 1243

Moriyaのspin-fluctuation theory

  T. Moriya and A. Kawabata:J. Phys. Soc. Jpn. 35 (1973) 669; ibid 34 (1973) 639.
  T. Moriya and Y. Takahashi: J.Phys. Soc. Jpn. Vol.45 (1978) 397.

1次元電子系

・bosonization
  S. Tomonaga, PTP Vol.13 No.5 pp.467-481 : Elementary Theory of Quantum-Mechanical Collective Motion of Particles, I, PTP Vol.13 No.5 pp.482-496 : Elementary Theory of Quantum-Mechanical Collective Motion of Particles, II
  V.J. Emery, in Highly Conducting One-Dimensional Solids (Plenum, 19xx)
  Luther
・g-ology + renormalization group
  J. Solyom: Adv. Phys. 28 (1979) 201
・Tomonaga-Luttinger模型
・位相ハミルトニアン
  H. Fukuyama and H. Takayama, in Electronic Properties of Inorganic Quasi-One-Dimensional Materials (D.Reidel, 1985)

2次元電子系と量子ホール効果

  R. B. Laughlin: Phys. Rev. Lett. 50, 1395-1398 (1983)

輸送現象

・Boltzmann方程式
・disordered system
・CPA
  F. Yonezawa, PTP Vol.40 No.4 pp.734-757 : A Systematic Approach to the Problems of Random Lattices. I;
  Mitsunobu Nakamura and Fumiko Yonezawa, PTP Vol.47 No.4 pp.1124-1139 : A Systematic Approach to the Problems of Random Lattices. II
  P. L. Leath Self-Consistent-Field Approximations in Disordered Alloys Phys. Rev. 171, 725-727 (1968)
・Anderson局在
  P. W. Anderson, Absence of Diffusion in Certain Random Lattices, Phys. Rev. 109, 1492-1505 (1958)
  P.A. Lee and T.V. Ramakrishnan, Rev. Mod. Phys. 57 (1985) 287
  Y. Nagaoka(ed): Prog. Theor. Phys. Suppl. 84 (1985)

近藤問題

・近藤効果
  J. Kondo,"Resistance Minimum in Dilute Magnetic Alloys", Prog. Theor. Phys. 32 (1964) 37.
  Y. Nagaoka, "Self-consistent Treatment of Kondo's Effect in Dilute Alloys", Phys. Rev. 138 (1965) A1112.
・s-d模型
・アンダーソン模型
   P. W. Anderson: "Localized Magnetic States in Metals", Phys. Rev. 124 (1961) 41.
   P. W. Anderson: "Ground State of a Magnetic Impurity in a Metal", Phys. Rev. 164 (1967) 352.
  P. Nozieres and C. T. Dominicis, "Singularities in the X-Ray Absorption and Emission of Metals. III. One-Body Theory Exact Solution", Phys. Rev. 178 (1969) 1097.
・Schrieffer-Wolff変換
  J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149, 491-492 (1966)
・軌道縮退アンダーソン模型の1/N展開,NCA近似
  Rasul and Hewson
  Y. Kuramoto
  P. Coleman
  N.E. Bickers: Rev. Mod. Phys. 59 (1987) 845.
・Bethe仮説による解法
  N. Andrei, Diagonalization of the Kondo Hamiltonian, Phys. Rev. Lett. 45, 379-382 (1980)
  N. Kawakami and A. Okiji, Phys. Lett. 80A, 163 (1980).
  AM Tsvelick, PB Wiegmann, Exact results in the theory of magnetic alloys, Advances in Physics, 1983

Hubbard模型

・Gutzwillerの変分法
  C. Gutzwiller: Correlation of Electrons in a Narrow s Band, Phys. Rev. 137, A1726-A1735 (1965)
  D. Vollhardt: Normal 3He: an almost localized Fermi liquid, Rev. Mod. Phys. 56, 99-120 (1984)
・金森近似
  J. Kanamori: PTP Vol.30 No.3 pp.275-289, Electron Correlation and Ferromagnetism of Transition Metals
・Hubbard近似 I, III
  J. Hubbard: "Electron correlations in narrow energy bands", Proc. Roy. Soc. (London) A276 (1963) 238; ibid A281(1964) 401.
・1次元の厳密解
E. H. Lieb and F. Y. Wu, Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension, Phys. Rev. Lett. 20, 1445-1448 (1968)
・無限次元の厳密解
W. Metzner and D. Vollhardt, Correlated Lattice Fermions in d=∞ Dimensions, Phys. Rev. Lett. 62, 324-327 (1989)

周期アンダーソン模型

d-p 模型

t-J模型

Slave boson法,Slave fermion法

モンテカルロ法

量子モンテカルロ法

  Masuo Suzuki, PTP Vol.56 No.5 pp.1454-1469 : Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems
  Masuo Suzuki, Seiji Miyashita and Akira Kuroda, PTP Vol.58 No.2 pp.701-702 : New Method of Monte Carlo Simulations and Phenomenological Theory of Phase Transition in the Two-Dimensional XY-Model
  J. E. Hirsch, R. L. Sugar, D. J. Scalapino, and R. Blankenbecler, Monte Carlo simulations of one-dimensional fermion systems, Phys. Rev. B 26, 5033-5055 (1982)

スピン・グラス

  G. Parigi:Infinite Number of Order Parameters for Spin-Glasses, Phys. Rev. Lett. 43, 1754-1756 (1979)
  S. Kirkpatrick and D. Sherrington, Infinite-ranged models of spin-glasses, Phys. Rev. B 17, 4384-4403 (1978)