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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C.W. Groth, M. Wimmer, A.R. Akhmerov, J. Tworzydło, C.W.J. Beenakker, Phys. Rev. Lett. 103, 196805 (2009). https://doi.org/10.1103/PhysRevLett.103.196805
K. Kobayashi, T. Ohtsuki, K.I. Imura, I.F. Herbut, Phys. Rev. Lett. 112, 016402 (2014). https://doi.org/10.1103/PhysRevLett.112.016402
T. Morimoto, A. Furusaki, C. Mudry, Phys. Rev. B 91, 235111 (2015). https://doi.org/10.1103/PhysRevB.91.235111
D. Bagrets, A. Altland, A. Kamenev, Phys. Rev. Lett. 117, 196801 (2016). https://doi.org/10.1103/PhysRevLett.117.196801
S. Seo, X. Lu, J.X. Zhu, R.R. Urbano, N. Curro, E.D. Bauer, V.A. Sidorov, L.D. Pham, T. Park, Z. Fisk, J.D. Thompson, Nat. Phys. 10, 120 (2014). https://doi.org/10.1038/nphys2820
P. Yunker, Z. Zhang, A.G. Yodh, Phys. Rev. Lett. 104, 015701 (2010). https://doi.org/10.1103/PhysRevLett.104.015701
P.W. Anderson, Phys. Rev. 109, 1492 (1958). https://doi.org/10.1103/PhysRev.109.1492
J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, A. Aspect, Nature 453, 891 (2008). https://doi.org/10.1038/nature07000
L. Balents, M.P.A. Fisher, Phys. Rev. B 56, 12970 (1997). https://doi.org/10.1103/PhysRevB.56.12970
D.G. Shelton, A.M. Tsvelik, Phys. Rev. B 57, 14242 (1998). https://doi.org/10.1103/PhysRevB.57.14242
V.V. Mkhitaryan, M.E. Raikh, Phys. Rev. Lett. 106, 256803 (2011). https://doi.org/10.1103/PhysRevLett.106.256803
Y.G. Sinai, Theory Probab. Appl. 27, 256 (1982). https://doi.org/10.1137/1127028
J.P. Bouchaud, A. Comtet, A. Georges, P. Le Doussal, Ann. Phys. 201, 285 (1990). https://doi.org/10.1016/0003-4916(90)90043-N
A. Comtet, D.S. Dean, J. Phys. A 31, 8595 (1998). https://doi.org/10.1088/0305-4470/31/43/004
A. Yosprakob, S. Suwanna, arXiv:1601.03827 (2016)
M. Steiner, M. Fabrizio, A.O. Gogolin, Phys. Rev. B 57, 8290 (1998). https://doi.org/10.1103/PhysRevB.57.8290
S. Succi, R. Benzi, Physica D 69, 327 (1993). https://doi.org/10.1016/0167-2789(93)90096-J
S. Palpacelli, S. Succi, Phys. Rev. E 77, 066708 (2008). https://doi.org/10.1103/PhysRevE.77.066708
F. Fillion-Gourdeau, H.J. Herrmann, M. Mendoza, S. Palpacelli, S. Succi, Phys. Rev. Lett. 111, 160602 (2013). https://doi.org/10.1103/PhysRevLett.111.160602
P.J. Dellar, D. Lapitski, S. Palpacelli, S. Succi, Phys. Rev. E 83, 046706 (2011). https://doi.org/10.1103/PhysRevE.83.046706
S. Succi, EPL 109, 50001 (2015). https://doi.org/10.1209/0295-5075/109/50001
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”).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Mendl, C.B., Palpacelli, S., Kamenev, A., Succi, S. (2018). Quantum Lattice Boltzmann Study of Random-Mass Dirac Fermions in One Dimension. In: Angilella, G., Amovilli, C. (eds) Many-body Approaches at Different Scales. Springer, Cham. https://doi.org/10.1007/978-3-319-72374-7_26
Download citation
DOI: https://doi.org/10.1007/978-3-319-72374-7_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-72373-0
Online ISBN: 978-3-319-72374-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)