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Fractional Charge (and Statistics) in Luttinger Liquids

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Trends in Nanophysics

Part of the book series: Engineering Materials ((ENG.MAT.))

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Abstract

Charge fractionalization is the phenomenon where quasi-particle excitations in a many-particle system appear with non-integer values relative to the fundamental charge unit. Examples of such systems are known from field theoretical models and from physical realizations. Recently there has been an interest in charge fractionalization in one-dimensional systems described by Luttinger liquid theory. These are gapless systems and that gives rise to the question whether non-integer charges should be regarded as sharp in the same meaning as in a gapped system. In this talk I first give an introduction to charge fractionalization as an effect in gapped systems and discuss next in what sense the charge fractionalization effect is found in gapless Luttinger liquids. The talk is based on a recent paper with Mats Horsdal and Thors Hans Hansson (Phys. Rev B 80: 1153 27, 2009).

This is a written version of a talk given at the Joint IFIN-HH,ICTP, IAEA Workshop on Trends in Nanoscience: Theory, Experiment, Technology, in Sibiu, Romania, August 23-30, 2009.

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Notes

  1. 1.

    The space averaging actually suppresses the short wavelength rather than the high frequency contributions. In one dimension the difference is not important, but in higher dimensions an explicit frequency cutoff may be needed, as discussed in [28].

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Acknowledgments

Thanks to Mats Horsdal and Hans Hansson for useful comments on the manuscript.

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Authors and Affiliations

  1. Department of Physics, University of Oslo, N-0316, Oslo, Norway

    Jon Magne Leinaas

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  1. Jon Magne Leinaas
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Correspondence to Jon Magne Leinaas .

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Editors and Affiliations

  1. Physics (INFIM), National Institute of Materials, Atomistilor St. 105, Bucuresti, 077125, Romania

    Victor Bârsan

  2. Physics (INFIM), National Institute of Materials, Atomistilor St. 105, Bucuresti, 077125, Romania

    Alexandru Aldea

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Leinaas, J.M. (2010). Fractional Charge (and Statistics) in Luttinger Liquids. In: Bârsan, V., Aldea, A. (eds) Trends in Nanophysics. Engineering Materials. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12070-1_8

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