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Quantum phases and phase transitions of Mott insulators

  • Subir Sachdev
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 645)

Abstract

This article contains a theoretical overview of the physical properties of antiferromagnetic Mott insulators in spatial dimensions greater than one. Many such materials have been experimentally studied in the past decade and a half, and we make contact with these studies. Mott insulators in the simplest class have an even number of S=1/2 spins per unit cell, and these can be described with quantitative accuracy by the bond operator method: we discuss their spin gap and magnetically ordered states, and the transitions between them driven by pressure or an applied magnetic field. The case of an odd number of S=1/2 spins per unit cell is more subtle: here the spin gap state can spontaneously develop bond order (so the ground state again has an even number of S=1/2 spins per unit cell), and/or acquire topological order and fractionalized excitations. We describe the conditions under which such spin gap states can form, and survey recent theories of the quantum phase transitions among these states and magnetically ordered states. We describe the breakdown of the Landau-Ginzburg-Wilson paradigm at these quantum critical points, accompanied by the appearance of emergent gauge excitations.

Keywords

Bond Order Gauge Field Quantum Phasis Quantum Phase Transition Paramagnetic Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S. Taniguchi, T. Nishikawa, Y. Yasui, Y. Kobayashi, M. Sato, T. Nishioka, M. Kotani, and S. Sano, J. Phys. Soc. Jpn. 64, 2758 (1995).ADSCrossRefGoogle Scholar
  2. 2.
    G. Chaboussant, P. A. Crowell, L. P. Lévy, O. Piovesana, A. Madouri, and D. Mailly, Phys. Rev. B 55, 3046 (1997).ADSCrossRefGoogle Scholar
  3. 3.
    P. R. Hammar, D. H. Reich, C. Broholm, and F. Trouw, Phys. Rev. B 57, 7846 (1998).ADSCrossRefGoogle Scholar
  4. 4.
    M. B. Stone, Y. Chen, J. Rittner, H. Yardimci, D. H. Reich, C. Broholm, D. V. Ferraris, and T. Lectka, Phys. Rev. B 65, 064423 (2002).ADSCrossRefGoogle Scholar
  5. 5.
    H. Kageyama, K. Yoshimura, R. Stern, N. V. Mushnikov, K. Onizuka, M. Kato, K. Kosuge, C. P. Slichter, T. Goto, and Y. Ueda, Phys. Rev. Lett. 82, 3168 (1999).ADSCrossRefGoogle Scholar
  6. 6.
    H. Kageyama, M. Nishi, N. Aso, K. Onizuka, T. Yosihama, K. Nukui, K. Kodama, K. Kakurai, and Y. Ueda, Phys. Rev. Lett 84, 5876 (2000).ADSCrossRefGoogle Scholar
  7. 7.
    H. Tanaka, A. Oosawa, T. Kato, H. Uekusa, Y. Ohashi, K. Kakurai, and A. Hoser, J. Phys. Soc. Jpn. 70, 939 (2001).ADSCrossRefGoogle Scholar
  8. 8.
    A. Oosawa, M. Fujisawa, T. Osakabe, K. Kakurai, and H. Tanaka, J. Phys. Soc. Jpn 72, 1026 (2003).ADSCrossRefGoogle Scholar
  9. 9.
    Ch. Rüegg, N. Cavadini, A. Furrer, H.-U. Güdel, K. Krämer, H. Mutka, A. Wildes, K. Habicht, and P. Vorderwisch, Nature (London) 423, 62 (2003).ADSCrossRefGoogle Scholar
  10. 10.
    M. Matsumoto, B. Normand, T. M. Rice, and M. Sigrist, Phys. Rev. Lett. 89, 077203 (2002) and cond-mat/0309440.ADSCrossRefGoogle Scholar
  11. 11.
    R. Coldea, D. A. Tennant, A. M. Tsvelik, and Z. Tylezynski, Phys. Rev. Lett. 86, 1335 (2001).ADSCrossRefGoogle Scholar
  12. 12.
    R. Coldea, D. A. Tennant, and Z. Tylezynski, Phys. Rev. B 68, 134424 (2003).ADSCrossRefGoogle Scholar
  13. 13.
    Insulators with an even number of electrons per unit cell can be adiabatically connected to band insulators and so some readers may object to calling such materials ‘Mott insulators'. However, the very different energy scales of the spin and charge excitations in the experimental systems are best understood in the framework of the Mott theory and one regards the dimerization as a small, low energy, deformation. Following widely accepted practice, we will continue to label these materials Mott insulators.Google Scholar
  14. 14.
    S. Sachdev and R. N. Bhatt, Phys. Rev. B 41, 9323 (1990).ADSCrossRefGoogle Scholar
  15. 15.
    A. V. Chubukov and Th. Jolicoeur, Phys. Rev. B 44, 12050 (1991).ADSCrossRefGoogle Scholar
  16. 16.
    V. N. Kotov, O. Sushkov, Z. Weihong, and J. Oitmaa, Phys. Rev. Lett. 80 5790 (1998).ADSCrossRefGoogle Scholar
  17. 17.
    G. Misguich and C. Lhuillier in Frustrated spin systems. H. T. Diep ed., World-Scientific, Singapore (2003), cond-mat/0310405.Google Scholar
  18. 18.
    The theorem of E. H. Lieb, T. Schultz, and D. J. Mattis, Ann. Phys. (N.Y.) 16, 407 (1961) prohibits spin gap states in d=1 systems with S=1/2 per unit cell and no broken translational symmetry. For d>1, the topological order to be discussed in Sect. 9.5 enables evasion of these constraints, as discussed e.g. in Appendix A of T. Senthil, M. Vojta, and S. Sachdev, cond-mat/0305193. and in G. Misguich, C. Lhuillier, M. Mambrini, and P. Sindzingre. Euro. Phys. Jour. B 26, 167 (2002).ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    N. Read and S. Sachdev, Phys Rev. Lett. 62, 1694 (1989).ADSCrossRefGoogle Scholar
  20. 20.
    N. Read and S. Sachdev, Phys. Rev. B 42, 4568 (1990).ADSCrossRefGoogle Scholar
  21. 21.
    N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991).ADSCrossRefGoogle Scholar
  22. 22.
    S. Sachdev and N. Read. Int. J. Mod. Phys. B 5. 219 (1991): available online at http://onsager.physics.vale.edu/p34.pdf.ADSCrossRefGoogle Scholar
  23. 23.
    X. G. Wen, Phys. Rev. B 44, 2664 (1991).ADSCrossRefGoogle Scholar
  24. 24.
    C.-H. Chung, K. Voelker, and Y.-B Kim, Phys. Rev. B 68, 094412 (2003).ADSCrossRefGoogle Scholar
  25. 25.
    M. P. Gelfand, R. R. P. Singh, and D. A. Huse, Phys. Rev. B 40, 10801 (1989).ADSCrossRefGoogle Scholar
  26. 26.
    J. Callaway. Quantum Theory of the Solid State, Academic Press, New York (1974).Google Scholar
  27. 27.
    K. P. Schmidt and G. S. Uhrig. Phys. Rev. Lett. 90, 227204 (2003).ADSCrossRefGoogle Scholar
  28. 28.
    M. Matsumoto, C. Yasuda, S. Todo, and H. Takayama, Phys. Rev. B 65, 014407 (2002).ADSCrossRefGoogle Scholar
  29. 29.
    T. Sommer, M. Vojta, and K. W. Becker, Eur. Phys. J. B 23, 329 (2001)ADSCrossRefGoogle Scholar
  30. 30.
    D. Carpentier and L. Balents, Phys. Rev. B 65, 024427 (2002).ADSCrossRefGoogle Scholar
  31. 31.
    M. Itakura, J. Phys. Soc. Jpn. 72 74 (2003).ADSCrossRefGoogle Scholar
  32. 32.
    B. Normand and T. M. Rice Phys. Rev. B 54, 7180 (1996); Phys. Rev. B 56, 8760 (1997).ADSCrossRefGoogle Scholar
  33. 33.
    S. Chakravarty, B. I. Halperin, and D. R. Nelson, Phys. Rev. B 39, 2344 (1989).ADSCrossRefGoogle Scholar
  34. 34.
    K. Chen, A. M. Ferrenberg, and D. P. Landau, Phys. Rev. B 48, 3249 (1993).ADSCrossRefGoogle Scholar
  35. 35.
    S.-k Ma, Modern Theory of Critical Phenomena, W. A. Benjamin, Reading, Mass, (1976).Google Scholar
  36. 36.
    S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411 (1992).ADSCrossRefGoogle Scholar
  37. 37.
    A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994).ADSCrossRefGoogle Scholar
  38. 38.
    K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).ADSCrossRefGoogle Scholar
  39. 39.
    E. Demler, S. Sachdev, and Y. Zhang, Phys. Rev. Lett. 87, 067202 (2001). Y. Zhang, E. Demler, and S. Sachdev, Phys. Rev. B 66, 094501 (2002).ADSCrossRefGoogle Scholar
  40. 40.
    I. Affleck, Phys. Rev. B 41, 6697 (1990).ADSCrossRefGoogle Scholar
  41. 41.
    S. Sachdev, T. Senthil, and R. Shankar, Phys. Rev. B 50, 258 (1994).ADSCrossRefGoogle Scholar
  42. 42.
    M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989).ADSCrossRefGoogle Scholar
  43. 43.
    Y. Shindo and H. Tanaka. cond-mat/0310691.Google Scholar
  44. 44.
    M. Oshikawa, M. Yamanaka, and I. Affleck, Phys. Rev. Lett. 78, 1984 (1997).ADSCrossRefGoogle Scholar
  45. 45.
    H. Kageyama, K. Yoshimura, R. Stern, N. V. Mushnikov, K. Onizuka, M. Kato, K. Kosuge, C. P. Slichter, T. Goto, and Y. Ueda, Phys. Rev. Lett. 82, 3168 (1999); K. Onizuka, H. Kageyama, Y. Narumi, K. Kindo, Y. Ueda, and T. Goto. J. Phys. Soc. Jpn. 69, 1016 (2000); S. Miyahara, F. Becca, and F. Mila. Phys. Rev. B 68, 024401 (2003).ADSCrossRefGoogle Scholar
  46. 46.
    W. Shiramura, K. Takatsu, B. Kurniawan, H. Tanaka, H. Uekusa, Y. Ohashi, K. Takizawa, H. Mitamura, and T. Goto, J. Phys. Soc. Jpn. 67, 1548 (1998).ADSCrossRefGoogle Scholar
  47. 47.
    P. Fazekas, and P. W. Anderson, Philos. Mag. 30, 23 (1974).CrossRefGoogle Scholar
  48. 48.
    S. A. Kivelson, D. S. Rokhsar, and J. P. Sethna, Phys. Rev. B 35, 8865 (1987).ADSCrossRefGoogle Scholar
  49. 49.
    S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 1999).zbMATHGoogle Scholar
  50. 50.
    B. Berg, and M. Lüscher, Nucl. Phys. B 190, 412 (1981).ADSCrossRefGoogle Scholar
  51. 51.
    S. Sachdev and R. Jalabert, Mod. Phys. Lett. B 4, 1043 (1990); available online at http://onsager.physics.yale.edu/p.32.pdf.ADSCrossRefGoogle Scholar
  52. 52.
    S. Sachdev and K. Park, Annals of Physics, N. Y. 298, 58 (2002).ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    A. D'Adda, P. Di Vecchia, and M. Lüscher, Nucl. Phys. B 146, 63 (1978).ADSCrossRefGoogle Scholar
  54. 54.
    E. Witten, Nucl. Phys. B 149, 285 (1979).ADSCrossRefGoogle Scholar
  55. 55.
    S. Sachdev, Proceedings of the International Conference on Theoretical Physics, Paris, Annales Henri Poincare 4, 559 (2003).Google Scholar
  56. 56.
    J. Villain, J. Phys. (Paris) 36, 581 (1975).CrossRefGoogle Scholar
  57. 57.
    J. V. José, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Phys. Rev. B 16, 1217 (1977).ADSCrossRefGoogle Scholar
  58. 58.
    E. Fradkin and S. A. Kivelson, Mod. Phys. Lett. B 4, 225 (1990).ADSCrossRefGoogle Scholar
  59. 59.
    S. T. Chui and J. D. Weeks, Phys. Rev. B 14, 4978 (1976); D. S. Fisher and J. D. Weeks, Phys. Rev. Lett. 50, 1077 (1983); E. Fradkin Phys. Rev. B 28, 5338 (1983).ADSCrossRefGoogle Scholar
  60. 60.
    A. M. Polyakov, Gauge Fields and Strings, Harwood Academic, New York (1987).Google Scholar
  61. 61.
    I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987).ADSCrossRefGoogle Scholar
  62. 62.
    W. Zheng and S. Sachdev, Phys. Rev. B 40, 2704 (1989).ADSCrossRefGoogle Scholar
  63. 63.
    D. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988).ADSCrossRefGoogle Scholar
  64. 64.
    J.-S. Bernier, C.-H. Chung, Y. B. Kim, and S. Sachdev, cond-mat/0310504.Google Scholar
  65. 65.
    K. Rommelse and M. den Nijs, Phys. Rev. Lett. 59, 2578 (1987).ADSCrossRefGoogle Scholar
  66. 66.
    J.-B. Fouet, P. Sindzingre, and C. Lhuillier, Eur. Phys. J. B 20, 241 (2001).ADSCrossRefGoogle Scholar
  67. 67.
    W. Brenig and A. Honecker, Phys. Rev. B 64, 140407 (2002).CrossRefGoogle Scholar
  68. 68.
    J.-B. Fouet, M. Mambrini, P. Sindzingre, and C. Lhuillier, Phys. Rev. B 67, 054411 (2003).ADSCrossRefGoogle Scholar
  69. 69.
    C.-H. Chung, J. B. Marston, and S. Sachdev, Phys. Rev. B 64, 134407 (2001).ADSCrossRefGoogle Scholar
  70. 70.
    A. W. Sandvik, S. Daul, R. R. P. Singh, and D. J. Scalapino, Phys. Rev. Lett., 89, 247201 (2002).ADSCrossRefGoogle Scholar
  71. 71.
    C. Lannert, M. P. A. Fisher, and T. Senthil, Phys. Rev. B 63, 134510 (2001).ADSCrossRefGoogle Scholar
  72. 72.
    K. Park and S. Sachdev, Phys. Rev. B 65, 220405 (2002).ADSCrossRefGoogle Scholar
  73. 73.
    K. Harada, N. Kawashima, and M. Troyer, Phys. Rev. Lett. 90, 117203 (2003).ADSCrossRefGoogle Scholar
  74. 74.
    V. N. Kotov, J. Oitmaa, O. P. Sushkov, and Z. Weihong, Phys. Rev. B 60, 14613 (1999): R. R. P. Singh, Z. Weihong, C. J. Hamer, and J. Oitmaa, Phys. Rev. B 60, 7278 (1999): V. N. Kotov and O. P. Sushkov. Phys. Rev. B 61. 11820 (2000): O. P. Sushkov, J. Oitmaa, and Z. Weihong, Phys. Rev. B 66, 054401 (2002).ADSCrossRefGoogle Scholar
  75. 75.
    M. S. L. du Croo de Jongh, J. M. J. van Leeuwen, and W. van Saarloos, Phys. Rev. B 62, 14844 (2000).ADSCrossRefGoogle Scholar
  76. 76.
    E. Dagotto and A. Morco, Phys. Rev. Lett. 63, 2148 (1989); R. R. P. Singh and R. Narayanan. Phys. Rev. Lett. 65, 1072 (1990): H. J. Schulz and T. A. L. Zlman. Europhys. Lett. 18, 355 (1992): H. J. Schulz, T. A. L. Ziman, and D. Poilblane, J. Phys. 1 (France) 6, 675 (1996).ADSCrossRefGoogle Scholar
  77. 77.
    L. Capriotti, F. Becca, A. Parola, and S. Sorella. Phys. Rev. Lett. 87, 097201 (2001).ADSCrossRefGoogle Scholar
  78. 78.
    O. P. Sushkov, Phys. Rev. B 63, 174429 (2001).ADSCrossRefGoogle Scholar
  79. 79.
    R. Eder and Y. Ohta. cond-mat/0304554 and cond-mat/0308184.Google Scholar
  80. 80.
    T. Senthil. A. Vishwanath, L. Balents. S. Sachdev, and M. P. A. Fisher, to appear in Science, cond-mat/0311326.Google Scholar
  81. 81.
    T. Senthil. L. Balents. S. Sachdev. A. Vishwanath, M. P. A. Fisher. cond-mat/0312617.Google Scholar
  82. 82.
    O. Motrunich and A. Vishwanath. cond-mat/0311222.Google Scholar
  83. 83.
    M. Vojta and S. Sachdev. Phys. Rev. Lett. 83, 3916 (1999); M. Vojta, Y. Zhang. and S. Sachdev, Phys. Rev. B 62, 6721 (2000).ADSCrossRefGoogle Scholar
  84. 84.
    C. Dasgupta and B. I. Halperin, Phys. Rev. Lett. 47, 1556 (1981).ADSCrossRefGoogle Scholar
  85. 85.
    See e. g. D. J. Amit: Field theory, the renormalization group, and critical phenomena. World Scientific, Singapore (1984).Google Scholar
  86. 86.
    H. Kleinert, F. S. Nogneira, and A. Sudbo, Phys. Rev. Lett. 88, 232001 (2002): Nucl. Phys. B 666. 316 (2003).ADSCrossRefGoogle Scholar
  87. 87.
    N. Nagaosa and P. A. Lee, Phys. Rev. B 61, 9166 (2000).ADSCrossRefGoogle Scholar
  88. 88.
    For completeness, we mention that the mapping to the dual XY model in a field has been questioned in I. Ichinose. T. Matsui, and M. Onoda, Phys. Rev. B 64, 104516 (2001), and [86]. The duality mappings in [80, 81] do not support these claims.ADSCrossRefGoogle Scholar
  89. 89.
    F. D. M. Haldane, Phys. Rev. Lett. 61, 1029 (1988).ADSMathSciNetCrossRefGoogle Scholar
  90. 90.
    J. M. Carmona, A. Pelissetto, and E. Vicari, Phys. Rev. B 61, 15136 (2000).ADSCrossRefGoogle Scholar
  91. 91.
    N. Arkani-Hamed, A. G. Cohen, and H. Georgi, Phys. Rev. Lett. 86, 4757 (2001): C. T. Hill. S. Pokorski, and J. Wang. Phys. Rev. D 64 105005 (2001).ADSMathSciNetCrossRefGoogle Scholar
  92. 92.
    G. Murthy and S. Sachdev, Nucl. Phys. B 344, 557 (1990).ADSMathSciNetCrossRefGoogle Scholar
  93. 93.
    R. Moessner and S. L. Sondhi, Phys. Rev. Lett. 86, 1881 (2001).ADSCrossRefGoogle Scholar
  94. 94.
    A. Angelucci, Phys. Rev. B 45, 5387 (1992).ADSCrossRefGoogle Scholar
  95. 95.
    A. V. Chubukov, T. Senthil and S. Sachdev. Phys. Rev. Lett. 72, 2089 (1994).ADSCrossRefGoogle Scholar
  96. 96.
    S. Sachdev, Phys. Rev. B 45, 12377 (1992).ADSCrossRefGoogle Scholar
  97. 97.
    T. Senthil and M. P. A. Fisher. Phys. Rev. B 62, 7850 (2000).ADSCrossRefGoogle Scholar
  98. 98.
    P. Azaria, B. Delamott, and T. Jolicoeur. Phys. Rev. Lett. 64, 3175 (1990): P. Azaria, B. Delamott and D. Mouhanna. Phys. Rev. Lett. 68, 1762 (1992).ADSCrossRefGoogle Scholar
  99. 99.
    N. Read and B. Chakraborty. Phys. Rev. B 40, 7133 (1989).ADSCrossRefGoogle Scholar
  100. 100.
    R. Jalabert and S. Sachdev. Phys. Rev. B 44, 686 (1991).ADSCrossRefGoogle Scholar
  101. 101.
    S. Sachdev and M. Vojta. J. Phys. Soc. Jpn. 69, Suppl. B, 1 (2000).Google Scholar
  102. 102.
    A. Vishwanath, L. Balents, and T. Senthil, cond-mat/0311085.Google Scholar
  103. 103.
    E. Fradkin, D. A. Huse, R. Moessner. V. Oganesyan, and S. L. Sondhi, cond-mat/0311353; E. Ardonne, P. Fendley, and E. Fradkin, cond-mat/0311466.Google Scholar

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© Springer-Verlag 2004

Authors and Affiliations

  • Subir Sachdev
    • 1
  1. 1.Department of PhysicsYale UniversityNew HavenUSA

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