Quantum Lattice Boltzmann Study of Random-Mass Dirac Fermions in One Dimension

  • Ch. B. Mendl
  • S. Palpacelli
  • A. Kamenev
  • S. Succi
Chapter

Abstract

We study the time evolution of quenched random-mass Dirac fermions in one dimension by quantum lattice Boltzmann simulations. For nonzero noise strength, the diffusion of an initial wave packet stops after a finite time interval, reminiscent of Anderson localization. However, instead of exponential localization we find algebraically decaying tails in the disorder-averaged density distribution. These qualitatively match a \( x^{-3/2}\) decay, which has been predicted by analytic calculations based on zero-energy solutions of the Dirac equation.

Notes

Acknowledgements

This work is dedicated to Professor Norman H. March on the occasion of his 90th birthday, with our warmest congratulations on an outstanding career and best wishes for more to come in the future.

C.M. acknowledges support from the Alexander von Humboldt foundation via a Feodor Lynen fellowship, as well as support from the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Contract No. DE-AC02-76SF00515. A.K. was supported by NSF grant DMR-1608238. S.S. was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 306357 (ERC Starting Grant “NANO-JETS”).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Ch. B. Mendl
    • 1
  • S. Palpacelli
    • 2
  • A. Kamenev
    • 3
  • S. Succi
    • 4
    • 5
  1. 1.Stanford Institute for Materials and Energy SciencesSLAC National Accelerator Laboratory and Stanford UniversityMenlo ParkUSA
  2. 2.Hyperlean S.r.lAnconaItaly
  3. 3.W. I. Fine Theoretical Physics Institute and School of Physics and AstronomyUniversity of MinnesotaMinneapolisUSA
  4. 4.Istituto Applicazioni CalcoloCNRRomaItaly
  5. 5.Institute for Applied Computational Science, John Paulson school of Engineering and Applied SciencesHarvard UniversityCambridgeUSA

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