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Quantum Phase Transitions from Topology in Momentum Space

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Quantum Analogues: From Phase Transitions to Black Holes and Cosmology

Part of the book series: Lecture Notes in Physics ((LNP,volume 718))

Abstract

Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the low-energy corner does not depend on the complicated details of the system and is relatively simple.

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References

  1. H. Georgi, S.L. Glashow: Phys. Rev. Lett. 32, 438 (1974)

    Article  ADS  Google Scholar 

  2. H. Georgi, H.R. Quinn, S. Weinberg: Phys. Rev. Lett. 33, 451 (1974)

    Article  ADS  Google Scholar 

  3. G.E. Volovik, L.P. Gorkov: Sov. Phys. JETP 61, 843 (1985)

    Google Scholar 

  4. D. Vollhardt, P. Wölfle: The Superfluid Phases of Helium 3 (Taylor and Francis, London, 1990)

    Google Scholar 

  5. N.D. Mermin: Rev. Mod. Phys. 51, 591 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  6. G.E. Volovik: The Universe in a Helium Droplet (Clarendon Press, Oxford, 2003)

    MATH  Google Scholar 

  7. P. Horava: Phys. Rev. Lett. 95, 016405 (2005)

    Article  ADS  Google Scholar 

  8. V.A. Khodel, V.R. Shaginyan: JETP Lett. 51, 553 (1990)

    ADS  Google Scholar 

  9. G.E. Volovik: JETP Lett. 53, 222 (1991)

    ADS  Google Scholar 

  10. V.R. Shaginyan, A.Z. Msezane, M.Ya. Amusia: Phys. Lett. A 338, 393 (2005)

    Article  ADS  Google Scholar 

  11. V.A. Khodel, J.W. Clark, M.V. Zverev: ‘Thermodynamic properties of Fermi systems with flat single-particle spectra’ (cond-mat/0502292)

    Google Scholar 

  12. V.A. Khodel, M.V. Zverev, V.M. Yakovenko: Phys. Rev. Lett. 95, 236402 (2005)

    Article  ADS  Google Scholar 

  13. G.E. Volovik: JETP Lett. 59, 830 (1994)

    ADS  Google Scholar 

  14. S. Sachdev: Quantum Phase Transitions (Cambridge University Press, Cambridge, 2003)

    Google Scholar 

  15. I.M. Lifshitz: Sov. Phys. JETP 11, 1130 (1960); I.M. Lifshitz, M.Y. Azbel, M.I. Kaganov: Electron Theory of Metals (Consultant Press, New York, 1972)

    Google Scholar 

  16. G.E. Volovik: Exotic Properties of Superfluid 3He (World Scientific, Singapore, 1992)

    Google Scholar 

  17. F.R. Klinkhamer, G.E. Volovik: JETP Lett. 80, 343 (2004)

    Article  ADS  Google Scholar 

  18. F.R. Klinkhamer, G.E. Volovik: Int. J. Mod. Phys. A 20, 2795 (2005)

    Article  MATH  ADS  Google Scholar 

  19. V. Gurarie, L. Radzihovsky, A. V. Andreev: Phys. Rev. Lett. 94, 230403 (2005)

    Article  ADS  Google Scholar 

  20. S.S. Botelho, C.A.R. Sa de Melo: J. Low Temp. Phys. 140, 409 (2005)

    Article  ADS  Google Scholar 

  21. S.S. Botelho, C.A.R. Sa de Melo: Phys. Rev. B 71, 134507 (2005)

    Article  ADS  Google Scholar 

  22. L.S. Borkowski, C.A.R. Sa de Melo: “From BCS to BEC superconductivity: Spectroscopic consequences” (cond-mat/9810370)

    Google Scholar 

  23. R.D. Duncan, C.A.R. Sa de Melo: Phys. Rev. B 62, 9675 (2000)

    Article  ADS  Google Scholar 

  24. X.G. Wen, A. Zee: Phys. Rev. B 66, 235110 (2002)

    Article  ADS  Google Scholar 

  25. E. Gubankova: “Conditions for existence of neutral strange quark matter” (hep-ph/0507291) E. Gubankova, E. Mishchenko, F. Wilczek: Phys. Rev. Lett. 94, 110402 (2005) K. Rajagopal, A. Schmitt: Phys. Rev. D73, 045003 (2006) R. Casalbuoni: “Color Superconductivity in High Density QCD' (hepph/0512198)

    Article  ADS  Google Scholar 

  26. N. Bergeal, J. Lesueur, M. Aprili, G. Faini, J. P. Contour, B. Leridon: “Direct test of pairing fluctuations in the pseudogap phase of underdoped cuprates” (cond-mat/0601265)

    Google Scholar 

  27. M.V. Sadovskii: “Models of the pseudogap state in high temperature superconductors” (cond-mat/0408489)

    Google Scholar 

  28. E.Z. Kuchinskii, M.V. Sadovskii: JETP 103, 415 (2006)

    Article  ADS  Google Scholar 

  29. J. von Neumann, E. Wigner: Phys. Zeit. 30, 467 (1929)

    Google Scholar 

  30. A.J. Stone: Proc. R. Soc. London A 351, 141 (1976)

    Article  ADS  Google Scholar 

  31. V.I. Arnold: Mathematical Method in Classical Mechanics (Nauka, Moscow, 1979, in Russian) (Springer-Verlag, 1989)

    Google Scholar 

  32. M.V. Berry: Proc. R. Soc. London A 392, 45 (1984)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. S.P. Novikov: Sov. Phys. Math. Dokl. 23, 298 (1981)

    MATH  Google Scholar 

  34. G.E. Volovik: JETP Lett. 46, 98 (1987)

    ADS  Google Scholar 

  35. H.B. Nielsen, M. Ninomiya: Nucl. Phys. B 185, 20 (1981); Nucl. Phys. B 193, 173 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  36. X.G. Wen: Phys. Rev. Lett. 88, 011602 (2002)

    Article  ADS  Google Scholar 

  37. F.R. Klinkhamer: Int. J. Mod. Phys. A21, 161 (2006); F.R. Klinkhamer: Nucl. Phys. B (Proc. Suppl.) 149, 209 (2005)

    ADS  Google Scholar 

  38. K. Kajantie, M. Laine, K. Rummukainen, M. Shaposhnikov: Phys. Rev. Lett. 77, 2887 (1996)

    Article  ADS  Google Scholar 

  39. S.L. Adler: “Anomalies to all orders”. In: Fifty Years of Yang-Mills Theory, ed. by G. 't Hooft (World Scientific, 2006)

    Google Scholar 

  40. E.I. Blount: Phys. Rev. B 32, 2935 (1985)

    Article  ADS  Google Scholar 

  41. H.J.H. Smilde, A.A. Golubov, Ariando, G. Rijnders, J.M. Dekkers, S. Harkema, D.H.A. Blank, H. Rogalla, H. Hilgenkamp, Phys. Rev. Lett. 95, 257001 (2005)

    Article  ADS  Google Scholar 

  42. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov: Nature 438, 197 (2005)

    Article  ADS  Google Scholar 

  43. S.G. Sharapov, V.P. Gusynin, H. Beck: Phys. Rev. B 69, 075104 (2004)

    Article  ADS  Google Scholar 

  44. K.S. Novoselov, E. McCann, S.V. Morozov, V.I. Falko, M.I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, A.K. Geim: Nature Physics 2, 177 (2006)

    Article  ADS  Google Scholar 

  45. E. McCann, V.I. Fal'ko: Phys. Rev. Lett. 96, 086805 (2006)

    Article  ADS  Google Scholar 

  46. M. Sato: Phys. Rev. B73, 214502 (2006)

    ADS  Google Scholar 

  47. A.A. Kordyuk, S.V. Borisenko, A.N. Yaresko, S.-L. Drechsler, H. Rosner, T.K. Kim, A. Koitzsch, K.A. Nenkov, M. Knupfer, J. Fink, R. Follath, H. Berger, B. Keimer, S. Ono, Yoichi Ando: Phys. Rev. B 70, 214525 (2004); S.V. Borisenko, A.A. Kordyuk, V. Zabolotnyy, J. Geck, D. Inosov, A. Koitzsch, J. Fink, M. Knupfer, B. Buechner, V. Hinkov, C.T. Lin, B. Keimer, T. Wolf, S.G. Chiuzbaian, L. Patthey, R. Follath: Phys. Rev. Lett. 96, 117004 (2006); T. Yamasaki, K. Yamazaki, A. Ino, M. Arita, H. Namatame, M. Taniguchi, A. Fujimori, Z.-X. Shen, M. Ishikado, S. Uchida: “Unmasking the nodal quasiparticle dynamics in cuprate superconductors using low-energy photoemission,” (cond-mat/0603006)

    Article  ADS  Google Scholar 

  48. G.E. Volovik: JETP Lett. 73, 162 (2001)

    Article  ADS  Google Scholar 

  49. F.R. Klinkhamer: Phys. Rev. D 73, 057301 (2006)

    Article  ADS  Google Scholar 

  50. G.E. Volovik: JETP Lett. 58, 469 (1993)

    ADS  Google Scholar 

  51. H. Balci, R.L. Greene: Phys. Rev. Lett. 93, 067001 (2004)

    Article  ADS  Google Scholar 

  52. W. Yu, B. Liang, R.L. Greene: Phys. Rev. B 72, 212512 (2005)

    Article  ADS  Google Scholar 

  53. K. Ishikawa, T. Matsuyama: Z. Phys. C 33, 41 (1986) K. Ishikawa, T. Matsuyama: Nucl. Phys. B 280, 523 (1987)

    Article  ADS  Google Scholar 

  54. G.E. Volovik, V.M. Yakovenko: J. Phys.: Condens. Matter 1, 5263 (1989)

    Article  ADS  Google Scholar 

  55. G.E. Volovik: “Fractional statistics and analogues of quantum Hall effect in superfluid 3He. lms”. In: Quantum Fluids and Solids - 1989 ed. by G.G. Ihas, Y. Takano (AIP Conference Proceedings, 1989) 194, pp. 136–146

    Google Scholar 

  56. Su-Peng Kou, Xiao-Liang Qi, Zheng-Yu Weng: Phys. Rev. B 72, 165114 (2005)

    Article  ADS  Google Scholar 

  57. D.T. Son, A.R. Zhitnitsky: Phys. Rev. D 70, 074018 (2004)

    Article  ADS  Google Scholar 

  58. O. Vafek and A. Melikyan: Phys. Rev. Lett. 96, 167005 (2006)

    Article  ADS  Google Scholar 

  59. G.E. Volovik: JETP Lett. 61, 958 (1995)

    ADS  Google Scholar 

  60. E.I. Rashba: “Spin-orbit coupling and spin transport” (cond-mat/0507007)

    Google Scholar 

  61. S.D.M. Haldane: Phys. Rev. Lett. 93, 206602 (2004)

    Article  ADS  Google Scholar 

  62. G.E. Volovik: JETP Lett. 64, 845 (1996)

    Article  ADS  Google Scholar 

  63. R. Jackiw, P. Rossi: Nucl. Phys. B 190, 681, (1981)

    Article  ADS  Google Scholar 

  64. M. Stone: Ann. Phys. 207, 38 (1991) X.G. Wen: Phys. Rev. B 43, 11025 (1991)

    Article  ADS  Google Scholar 

  65. M. Stone, R. Roy: Phys. Rev. B 69, 184511 (2004)

    Article  ADS  Google Scholar 

  66. J. Dziarmaga: Phys. Rev. Lett. 95 245701 (2005)

    Article  ADS  Google Scholar 

  67. J.R. Hook, H.E. Hall: J. Phys. C 12, 783 (1979) G.E. Volovik: JETP Lett. 27, 573 (1978)

    Article  ADS  Google Scholar 

  68. D.N. Paulson, M. Krusius, J.C. Wheatley: Phys. Rev. Lett. 36, 1322 (1976)

    Article  ADS  Google Scholar 

  69. A.G. Abanov, F. Franchini: Phys. Lett. A 316, 342 (2003)

    Article  MATH  ADS  Google Scholar 

  70. M. Fioroni, G. Immirzi: “How and why the wave function collapses after a measurement” (gr-qc/9411044)

    Google Scholar 

  71. W.H. Zurek, U. Dorner, P. Zoller: Phys. Rev. Lett. 95, 105701 (2005)

    Article  ADS  Google Scholar 

  72. M. Grady: “Spontaneous symmetry breaking as the mechanism of quantum measurement” (hep-th/9409049)

    Google Scholar 

  73. Ya.G. Sinai: Theory of Phase Transitions, International series in natural philosophy (Pergamon Press, 1983)

    Google Scholar 

  74. P.G. Grinevich, G.E. Volovik: J. Low Temp. Phys. 72, 371 (1988); M.M. Salomaa, G.E. Volovik: Phys. Rev. 37, 9298 (1988); M.M. Salomaa, G.E. Volovik: J. Low Temp. Phys. 74, 319 (1989)

    Article  ADS  Google Scholar 

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Author information

Authors and Affiliations

  1. Low Temperature Laboratory, Helsinki University of Technology, 2200, FIN-02015 HUT, Espoo, Finland

    G. E. Volovik

  2. Landau Institute for Theoretical Physics, Kosygina 2, 119334, Moscow, Russia

    G. E. Volovik

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  1. G. E. Volovik
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Editors and Affiliations

  1. Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, V6T1Z1, B.C., Canada

    William G. Unruh

  2. Institut für Theoretische Physik, Technische Universität Dresden, 01062, Dresden, Germany

    Ralf Schützhold

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Volovik, G. (2007). Quantum Phase Transitions from Topology in Momentum Space. In: Unruh, W.G., Schützhold, R. (eds) Quantum Analogues: From Phase Transitions to Black Holes and Cosmology. Lecture Notes in Physics, vol 718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-70859-6_3

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