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Annals of Physics
Volumn 310, Issue 2, 2004, Pages 428-492
A class of P, T-invariant topological phases of interacting electrons
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EID: 1842607210     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aop.2004.01.006     Document Type: Article
Times cited : (241)
References (101)
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    • Bosons and fermions are the only one-dimensional representations of the permutation group. In principle, higher-dimensional representations are possible, namely parastatistics. These representations can be interpreted in terms of bosons or fermions with some additional 'hidden' local quantum numbers. There is no topological character to these representations, and since these local quantum numbers are presumably measurable, this would not appear to be a useful arena for quantum computation. See
    • Bosons and fermions are the only one-dimensional representations of the permutation group. In principle, higher-dimensional representations are possible, namely parastatistics. These representations can be interpreted in terms of bosons or fermions with some additional 'hidden' local quantum numbers. There is no topological character to these representations, and since these local quantum numbers are presumably measurable, this would not appear to be a useful arena for quantum computation. See H.S. Green, Phys. Rev. 90 (1953) 270.
    • (1953) Phys. Rev. , vol.90 , pp. 270
    • Green, H.S.1
  • 17
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    • see also the discussion and several of the reprints in F. Wilczek (Ed.) Fractional Statistics and Anyon Superconductivity, World Scientific, Singapore 1990
    • F. Wilczek, Phys. Rev. Lett. 49 (1982) 957, see also the discussion and several of the reprints in F. Wilczek (Ed.) Fractional Statistics and Anyon Superconductivity, World Scientific, Singapore 1990.
    • (1982) Phys. Rev. Lett. , vol.49 , pp. 957
    • Wilczek, F.1
  • 40
    • 85030874998 scopus 로고    scopus 로고
    • unpublished notes
    • K. Walker, unpublished notes.
    • Walker, K.1
  • 64
    • 85030884991 scopus 로고    scopus 로고
    • quant-ph/0003128 and references therein
    • M.H. Freedman, quant-ph/0003128 and references therein.
    • Freedman, M.H.1
  • 65
  • 74
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    • Such a Hilbert space representation has been used in the context of quantum gravity
    • The similarity is greatest in 2+1 dimensions. See
    • Such a Hilbert space representation has been used in the context of quantum gravity. The similarity is greatest in 2+1 dimensions. See A. Ashtekar, V. Husain, C. Rovelli, J. Samuel, L. Smolin, Class. Quant. Grav. 6 (1989) 185.
    • (1989) Class. Quant. Grav. , vol.6 , pp. 185
    • Ashtekar, A.1    Husain, V.2    Rovelli, C.3    Samuel, J.4    Smolin, L.5
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    • third ed., Springer, Berlin, GTM 211
    • S. Lang, Algebra, third ed., Springer, Berlin, 2002, GTM 211.
    • (2002) Algebra
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    • in preparation
    • M. Freedman, et al., in preparation.
    • Freedman, M.1
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    • Physically measurable correlation functions in 2D statistical mechanical models always combine the conformal blocks of the holomorphic and antiholomorphic parts of the theory in just such a way that the result is single-valued
    • Physically measurable correlation functions in 2D statistical mechanical models always combine the conformal blocks of the holomorphic and antiholomorphic parts of the theory in just such a way that the result is single-valued.
  • 90
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    • For the q > 4 Potts model this is easily remedied, however. A first order transition becomes continuous after the introduction of an arbitrary small disorder [61,62]. The size of the clusters diverges at the self-dual point [63,64] and therefore the surrounding loops remain long
    • For the q > 4 Potts model this is easily remedied, however. A first order transition becomes continuous after the introduction of an arbitrary small disorder [61,62]. The size of the clusters diverges at the self-dual point [63,64] and therefore the surrounding loops remain long.
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    • cond-mat/9806355
    • J. Cardy, cond-mat/9806355, 1998.
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    • However, these arguments do apply to four dimensions. If a magnetic field is imposed, Landau levels form, and there is one-dimensional dispersion in the direction parallel to the magnetic field, and one can define right- and left-moving fields with respect to this direction. Therefore, an electric field parallel to the magnetic field causes a flow of current in this direction, and there is a chiral anomaly proportional to E · B
    • However, these arguments do apply to four dimensions. If a magnetic field is imposed, Landau levels form, and there is one-dimensional dispersion in the direction parallel to the magnetic field, and one can define right- and left-moving fields with respect to this direction. Therefore, an electric field parallel to the magnetic field causes a flow of current in this direction, and there is a chiral anomaly proportional to E · B.

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