Disordered Quantum Solids

  • T. Giamarchi
  • E. Orignac
Chapter
Part of the NATO Science Series book series (NAII, volume 23)

Abstract

Due to the peculiar non-Fermi liquid of one dimensional systems, disorder has particularly strong effects. We show that such systems belong to the more general class of disordered quantum solids. We discuss the physics of such disordered interacting systems and the methods that allows to treat them. In addition to, by now standard renormalization group methods, We explain how a simple variational approach allows to treat these problems even in case when the RG fails. We discuss various physical realizations of such disordered quantum solids both in one and higher dimensions (Wigner crystal, Bose glass). We investigate in details the interesting example of a disordered Mott insulator and argue that intermediate disorder can lead to a novel phase, the Mott glass, intermediate between a Mott and and Anderson insulator.

Keywords

Spin Chain Optical Conductivity Charge Density Wave Localization Length Mott Insulator 
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References

  1. [1]
    T. Giamarchi and E. Orignac cond-mat/0005220; to be published by Springer in “Theoretical methods for strongly correlated electrons”, CRM Series in Mathematical Physics.Google Scholar
  2. [2]
    N. F. Mott and W. D. Twose, Adv. Phys. 10, 107 (1961).ADSCrossRefGoogle Scholar
  3. [3]
    V. L. Berezinskii, Sov. Phys. JETP 38, 620 (1974).ADSGoogle Scholar
  4. [4]
    A. A. Abrikosov and J. A. Rhyzkin, Adv. Phys. 27, 147 (1978).ADSCrossRefGoogle Scholar
  5. [5]
    E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).ADSCrossRefGoogle Scholar
  6. [6]
    F. Wegner, Z. Phys. B 35, 207 (1979).ADSCrossRefGoogle Scholar
  7. [7]
    K. B. Efetov, A. I. Larkin, and D. E. Khmel’nitskii, Sov. Phys. JETP 52, 568 (1980).ADSGoogle Scholar
  8. [8]
    K. B. Efetov, Adv. Phys. 32, 53 (1983).MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    P. Nozieres, Theory of Interacting Fermi systems (W. A. Benjamin, New York, 1961).Google Scholar
  10. [10]
    B. L. Altshuler and A. G. Aronov, in Electron-electron interactions in disordered systems, edited by A.L. Efros and M. Pollak (North-Holland, Amsterdam, 1985).Google Scholar
  11. [11]
    A. M. Finkelstein, Z. Phys. B 56, 189 (1984).ADSCrossRefGoogle Scholar
  12. [12]
    P. A. Lee and T. V. Ramakhrishnan, Rev. Mod. Phys. 57, 287 (1985).ADSCrossRefGoogle Scholar
  13. [13]
    For a review see: D. Belitz and T. R. Kirkpatrick, Rev. Mod. Phys. 66 261 (1994).ADSCrossRefGoogle Scholar
  14. [14]
    J. Sólyom, Adv. Phys. 28, 209 (1979).CrossRefGoogle Scholar
  15. [15]
    V. J. Emery, in Highly Conducting One-Dimensional Solids, edited by J. T. Devreese and al. (Plenum, New York, 1979), p. 327.Google Scholar
  16. [16]
    H. J. Schulz, in Mesoscopic quantum physics, Les Houches LXI, edited by E. Akkermans, G. Montambaux, J. L. Pichard, and J. Zinn-Justin (Elsevier, Amsterdam, 1995).Google Scholar
  17. [17]
    J. Voit, Rep. Prog. Phys. 58, 977 (1995).ADSCrossRefGoogle Scholar
  18. [18]
    D. Senechal, in “Theoretical methods for strongly correlated electrons”, CRM Series in Mathematical Physics, to be published by Springer.Google Scholar
  19. [19]
    P. Jordan and E. Wigner, Z. Phys. 47, 631 (1928).ADSMATHCrossRefGoogle Scholar
  20. [20]
    T. Giamarchi and H. J. Schulz, Europhys. Lett. 3, 1287 (1987).ADSCrossRefGoogle Scholar
  21. [21]
    T. Giamarchi and H. J. Schulz, Phys. Rev. B 37, 325 (1988).ADSCrossRefGoogle Scholar
  22. [22]
    M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989).ADSCrossRefGoogle Scholar
  23. [23]
    C. Doty and D. S. Fisher, Phys. Rev. B 45, 2167 (1992).ADSCrossRefGoogle Scholar
  24. [24]
    G. Grüner, Rev. Mod. Phys. 60, 1129 (1988).ADSCrossRefGoogle Scholar
  25. [25]
    H. Fukuyama, J. Phys. Soc. Jpn. 41, 513 (1976).ADSCrossRefGoogle Scholar
  26. [26]
    H. Fukuyama and P. A. Lee, Phys. Rev. B 17, 535 (1978).ADSCrossRefGoogle Scholar
  27. [27]
    M. V. Feigelmann and V. M. Vinokur, Phys. Lett. A 87, 53 (1981).ADSCrossRefGoogle Scholar
  28. [28]
    Y. Suzumura and H. Fukuyama, J. Phys. Soc. Jpn. 52, 2870 (1983).ADSCrossRefGoogle Scholar
  29. [29]
    L. P. Gorkov and I. E. Dzyaloshinski, JETP Lett. 18, 401 (1973).ADSGoogle Scholar
  30. [30]
    D. C. Mattis, J. Math. Phys. 15, 609 (1974).ADSCrossRefGoogle Scholar
  31. [31]
    A. Luther and I. Peschel, Phys. Rev. Lett. 32, 992 (1974).ADSCrossRefGoogle Scholar
  32. [32]
    W. Apel, J. Phys. C 15, 1973 (1982).ADSCrossRefGoogle Scholar
  33. [33]
    W. Apel and T. M. Rice, J. Phys. C 16, L271 (1982).CrossRefGoogle Scholar
  34. [34]
    W. Apel and T. M. Rice, Phys. Rev. B 26, 7063 (1982).ADSCrossRefGoogle Scholar
  35. [35]
    J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973).ADSCrossRefGoogle Scholar
  36. [36]
    J. M. Kosterlitz, J. Phys. C 7, 1046 (1974).ADSCrossRefGoogle Scholar
  37. [37]
    C. Kane and M. P. A. Fisher, Phys. Rev. Lett. 68, 1220 (1992).ADSCrossRefGoogle Scholar
  38. [38]
    C. Kane and M. P. A. Fisher, Phys. Rev. B 46, 15233 (1992).ADSCrossRefGoogle Scholar
  39. [39]
    T. Giamarchi and H. Maurey, in Correlated fermions and transport in mesoscopic systems, edited by T. Martin, G. Montambaux, and J. Tran Thanh Van (Editions Frontières, Gif sur Yvette, France, 1996), condmat/9608006.Google Scholar
  40. [40]
    F. D. M. Haldane, Phys. Rev. Lett. 47, 1840 (1981).ADSCrossRefGoogle Scholar
  41. [41]
    T. Giamarchi and B. S. Shastry, Phys. Rev. B 51, 10915 (1995).ADSCrossRefGoogle Scholar
  42. [42]
    H. Maurey and T. Giamarchi, Phys. Rev. B 51, 10833 (1995).ADSCrossRefGoogle Scholar
  43. [43]
    N. Kawakami and S. Fujimoto, Phys. Rev. B 52, 6189 (1995).ADSGoogle Scholar
  44. [44]
    E. Orignac and T. Giamarchi, Phys. Rev. B 56, 7167 (1997).ADSCrossRefGoogle Scholar
  45. [45]
    E. Orignac and T. Giamarchi, Phys. Rev. B 57, 11713 (1998).ADSCrossRefGoogle Scholar
  46. [46]
    V. Brunei and T. Jolicoeur, Phys. Rev. B 58, 8481 (1998).ADSCrossRefGoogle Scholar
  47. [47]
    E. Orignac and T. Giamarchi, Phys. Rev. B 57, 5812 (1998).ADSCrossRefGoogle Scholar
  48. [48]
    K. J. Runge and G. T. Zimanyi, Phys. Rev. B 49, 15212 (1994).ADSCrossRefGoogle Scholar
  49. [49]
    G. Bouzerar, D. Poilblanc, and G. Montambaux, Phys. Rev. B 49, 8258 (1994).CrossRefGoogle Scholar
  50. [50]
    G. Bouzerar and D. Poilblanc, Phys. Rev. B 52, 10772 (1995).ADSCrossRefGoogle Scholar
  51. [51]
    R. A. Römer and A. Punnoose, Phys. Rev. B 52, 14809 (1995).ADSCrossRefGoogle Scholar
  52. [52]
    R. Berkovits and Y. Avishai, Europhys. Lett. 29, 475 (1995).ADSCrossRefGoogle Scholar
  53. [53]
    S. Haas, J. Riera, and E. Dagotto, Phys. Rev. B 48, 13174 (1993).Google Scholar
  54. [54]
    R. T. Scalettar, G. G. Batrouni, and G. T. Zimanyi, Phys. Rev. Lett. 66, 3144 (1991).ADSCrossRefGoogle Scholar
  55. [55]
    S. R. White, Phys. Rev. B 48, 10345 (1993).ADSCrossRefGoogle Scholar
  56. [56]
    P. Schmitteckert et al., Phys. Rev. Lett. 80, 560 (1998).ADSCrossRefGoogle Scholar
  57. [57]
    M. Mézard and G. Parisi, J. de Phys. I 1, 809 (1991).Google Scholar
  58. [58]
    T. Giamarchi and P. Le Doussal, in Statics and dynamics of disordered elastic systems, edited by A. P. Young (World Scientific, Singapore, 1998), p. 321, cond-mat/9705096.Google Scholar
  59. [59]
    T. Giamarchi and P. Le Doussal, Phys. Rev. B 52, 1242 (1995).ADSCrossRefGoogle Scholar
  60. [60]
    J. L. Cardy and S. Ostlund, Phys. Rev. B 25, 6899 (1982).ADSCrossRefGoogle Scholar
  61. [61]
    P. Le Doussal and T. Giamarchi, Phys. Rev. Lett. 74, 606 (1995).ADSCrossRefGoogle Scholar
  62. [62]
    M. Mézard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and beyond (World Scientific, Singapore, 1987).MATHGoogle Scholar
  63. [63]
    A. I. Larkin, Sov. Phys. JETP 31, 784 (1970).ADSGoogle Scholar
  64. [64]
    A. I. Larkin and Y. N. Ovchinnikov, J. Low Temp. Phys 34, 409 (1979).ADSCrossRefGoogle Scholar
  65. [65]
    There are some subtleties for systems for which the size of the particles differs from the lattice spacing. This leads to the definitions of two characteristic lengths. We ignore these differences here since they do not occur for classical CDW and ID fermionic systems. See [58] for consequences for classical systems and [83] for the Wigner crystal.Google Scholar
  66. [66]
    Such a length was also obtained by Imry and Ma for the random field Ising model. So a proper acronym for this length might be the Loflim length (for Larkin-Ovchinikov, Fukuyama-Lee, Imry-Ma).Google Scholar
  67. [67]
    This remark is originally due to S. Sachdev.Google Scholar
  68. [68]
    T. Giamarchi and P. Le Doussal, Phys. Rev. B 53, 15206 (1996).ADSCrossRefGoogle Scholar
  69. [69]
    A. Georges, O. Parcollet and S. Sachdev, cond-mat/9909239.Google Scholar
  70. [70]
    A. L. Efros and B. I. Shklovskii, J. Phys. C 8, L49 (1975).ADSCrossRefGoogle Scholar
  71. [71]
    P. A. Lee and A. I. Larkin, Phys. Rev. B 17, 1596 (1978).Google Scholar
  72. [72]
    L. V. Keldysh, Sov. Phys. JETP 20, 1018 (1965), [Zh. Eksp. Teor. Fiz. 47 1515(1964)].MathSciNetGoogle Scholar
  73. [73]
    G.-Z. Zhou, Z. bin Su, B. lin Hao, and L. Yu, Phys. Rep. 118, 1 (1985).MathSciNetADSCrossRefGoogle Scholar
  74. [74]
    J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986).ADSCrossRefGoogle Scholar
  75. [75]
    A. Kamenev and A. Andreev, Phys. Rev. B 60, 2218 (1999), condmat/9810191.ADSCrossRefGoogle Scholar
  76. [76]
    P. C. Martin, E. D. Siggia, and H. A. Rose, Phys. Rev. A 8, 423 (1973).Google Scholar
  77. [77]
    P. Chauve, T. Giamarchi, and P. Le Doussal, Europhys. Lett. 44, 110 (1998).ADSCrossRefGoogle Scholar
  78. [78]
    P. Chauve, T. Giamarchi, and P. Le Doussal, Phys. Rev. B 62, 6241 (2000).ADSCrossRefGoogle Scholar
  79. [79]
    P. Chauve, P. Le Doussal, and T. Giamarchi, Phys. Rev. B 61, R11906 (2000).ADSCrossRefGoogle Scholar
  80. [80]
    J. P. Bouchaud, L. F. Cugliandolo, J. Kurchan, and M. Mézard, in Spin Glasses and random fields, edited by A. P. Young (World Scientific, Singapore, 1997), cond-mat/9704096.Google Scholar
  81. [81]
    L. F. Cugliandolo and G. Lozano, Real-time non-equilibrium dynamics of quantum glassy systems, 1998, cond-mat/9807138.Google Scholar
  82. [82]
    D. R. Nelson and V. M. Vinokur, Phys. Rev. B 48, 13060 (1993).ADSCrossRefGoogle Scholar
  83. [83]
    R. Chitra, T. Giamarchi, and P. Le Doussal, Phys. Rev. Lett. 80, 3827 (1998).ADSGoogle Scholar
  84. [84]
    R. Chitra, T. Giamarchi and P. Le Doussal, to be published.Google Scholar
  85. [85]
    A. A. Gogolin, Phys. Rep. 86, 1 (1982).MathSciNetADSCrossRefGoogle Scholar
  86. [86]
    A. Comtet, A. Georges, and P. Le Doussal, Phys. Lett. B 208, 487 (1988).ADSCrossRefGoogle Scholar
  87. [87]
    A. O. Gogolin, A. A. Nersesyan, A. M. Tsvelik, and L. Yu, Nucl. Phys. B 540, 705 (1997).Google Scholar
  88. [88]
    L. Balents and M. P. A. Fisher, Phys. Rev. B 56, 12970 (1997).ADSCrossRefGoogle Scholar
  89. [89]
    T. P. Eggarter and R. Riedinger, Phys. Rev. B 18, 569 (1978).ADSCrossRefGoogle Scholar
  90. [90]
    K. Damle, O. Motrunich, and D. A. Huse, Phys. Rev. Lett. 84, 3434 (2000).ADSCrossRefGoogle Scholar
  91. [91]
    D. S. Fisher, Phys. Rev. B 50, 3799 (1994).ADSCrossRefGoogle Scholar
  92. [92]
    D. S. Fisher, Phys. Rev. B 51, 6411 (1995).ADSCrossRefGoogle Scholar
  93. [93]
    R. Shankar, Int. J. Mod. Phys. B 4, 2371 (1990).ADSCrossRefGoogle Scholar
  94. [94]
    S. Fujimoto and N. Kawakami, Phys. Rev. B 54, R11018 (1996).ADSCrossRefGoogle Scholar
  95. [95]
    M. Mori and H. Fukuyama, J. Phys. Soc. Jpn. 65, 3604 (1996).ADSCrossRefGoogle Scholar
  96. [96]
    M. A. Paalanen, J. E. Graebner, R. N. Bhatt, and S. Sachdev, Phys. Rev. Lett. 61, 597 (1988).ADSCrossRefGoogle Scholar
  97. [97]
    B. Grenier et al., Phys. Rev. B 57, 3444 (1998).ADSCrossRefGoogle Scholar
  98. [98]
    E. Orignac and T. Giamarchi, Phys. Rev. B 56 7167 (1997); 57 5812 (1998).ADSCrossRefGoogle Scholar
  99. [99]
    M. Azuma and et al., Phys. Rev. B 55, 8658 (1997).ADSCrossRefGoogle Scholar
  100. [100]
    S. A. Carter et al., Phys. Rev. Lett. 77, 1378 (1996).ADSCrossRefGoogle Scholar
  101. [101]
    S. Fujimoto and N. Kawakami, Phys. Rev. B 56, 9360 (1997).ADSCrossRefGoogle Scholar
  102. [102]
    C. Monthus, O. Golinelli, and T. Jolicoeur, Phys. Rev. B 58, 805 (1998).CrossRefGoogle Scholar
  103. [103]
    T. Giamarchi, Physica B 230-232, 975 (1997).ADSCrossRefGoogle Scholar
  104. [104]
    E. Orignac, T. Giamarchi, and P. L. Doussal, Phys. Rev. Lett. 83, 2378 (1999).ADSCrossRefGoogle Scholar
  105. [105]
    T. Giamarchi, P. Le Doussal and E. Orignac, to be published.Google Scholar
  106. [106]
    H. J. Schulz, Phys. Rev. Lett. 71, 1864 (1993).ADSCrossRefGoogle Scholar
  107. [107]
    For small bounded disorder the gap of the Mott insulator phase is robust.Google Scholar

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© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • T. Giamarchi
  • E. Orignac

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