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Interaction-driven localization in holography

Nature Physics volume 9, pages 649–655 (2013)Cite this article

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Abstract

Interaction-driven charge localization across a quantum phase transition involves a fundamental rearrangement of the low-energy degrees of freedom. This fact challenges weakly interacting quasiparticle descriptions of the physics. The canonical example of such localization is the Mott transition. Here, we present a localization mechanism distinct from ‘Mottness’, which employs strong interactions in an essential way. Our mechanism allows anisotropic localization: phases can arise that are insulating in some directions and metallic in others. The central observation is that localization occurs if an operator that breaks translation invariance, a ‘generalized Umklapp’ operator, becomes relevant in the effective low-energy theory. This does not occur at weak coupling. We realize such localization in a strongly interacting theory described by means of the holographic correspondence. Our model captures key features of metal–insulator transitions including major spectral weight transfer and bad (incoherent) metallic behaviour in the vicinity of the transition. The localized phase has a power law gap in the optical conductivity.

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Figure 1
Figure 2: Two renormalization group flow scenarios that arise in our theories, mediating quantum phase transitions between metallic and insulating phases.
Figure 3: A quantum phase transition.
Figure 4: Spectral weight transfer.
Figure 5: Log–log plot of the d.c. resistivity as a function of temperature.

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Acknowledgements

We acknowledge helpful discussions with J. Gauntlett, G. Horowitz, S. Kivelson, S. Sachdev, D. Tong and J. Zaanen. S.A.H. is partially supported by a Sloan Research Fellowship and by a DOE Early Career Award.

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Authors and Affiliations

  1. Blackett Laboratory, Imperial College, London, SW7 2AZ, UK

    Aristomenis Donos

  2. Department of Physics, Stanford University, Stanford, California 94305-4060, USA

    Sean A. Hartnoll

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  1. Aristomenis Donos
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  2. Sean A. Hartnoll
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A.D. and S.A.H. were both involved in the conception, technical computations and writing up of this work.

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Correspondence to Sean A. Hartnoll.

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Donos, A., Hartnoll, S. Interaction-driven localization in holography. Nature Phys 9, 649–655 (2013). https://doi.org/10.1038/nphys2701

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