Skip to main content
SpringerLink
Log in
Book cover

Disorder-Free Localization pp 55–69Cite as

Localization

  • Chapter
  • First Online:

  • 364 Accesses

Part of the book series: Springer Theses ((Springer Theses))

Abstract

In this chapter we investigate the localization behaviour in our model in one and two dimensions. The localization of the fermions is diagnosed using global quantum quench protocols relevant to experiments. Spectral properties of the model also shed light on transient behaviour observed in these dynamical probes that is unique to binary disorder.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    The first order is zero since the overlap of eigenstates between separate runs is zero.

  2. 2.

    Note that in our definition of \(N_\text {half}\) we only sum over the initially empty sites in the 1D strip shown in Fig. 3.8c.

References

  1. Weiße A, Wellein G, Alvermann A, Fehske H (2006) The kernel polynomial method. Rev Mod Phys 78:275–306. https://doi.org/10.1103/RevModPhys.78.275

    Article  ADS  MathSciNet  Google Scholar 

  2. Kramer B, MacKinnon A (1993) Localization: theory and experiment. Rep Prog Phys 56:1469–1564. https://doi.org/10.1088/0034-4885/56/12/001

    Article  ADS  Google Scholar 

  3. Choi J-y, Hild S, Zeiher J, Schauss P, Rubio-Abadal A, Yefsah T, Khemani V, Huse DA, Bloch I, Gross C (2016) Exploring the many-body localization transition in two dimensions. Science (80-.) 352:1547–1552. https://doi.org/10.1126/science.aaf8834

    Article  ADS  MathSciNet  Google Scholar 

  4. Hauschild J, Heidrich-Meisner F, Pollmann F (2016) Domain-wall melting as a probe of many-body localization. Phys Rev B 94:161109. https://doi.org/10.1103/PhysRevB.94.161109

  5. Schreiber M, Hodgman SS, Bordia P, Luschen HP, Fischer MH, Vosk R, Altman E, Schneider U, Bloch I (2015) Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science (80-.) 349:842–845. https://doi.org/10.1126/science.aaa7432

    Article  ADS  MathSciNet  Google Scholar 

  6. Bordia P, Lüschen H, Scherg S, Gopalakrishnan S, Knap M, Schneider U, Bloch I (2017) Probing slow relaxation and many-body localization in two-dimensional quasiperiodic systems. Phys Rev X 7:041047. https://doi.org/10.1103/PhysRevX.7.041047

  7. Smith A, Knolle J, Moessner R, Kovrizhin DL (2018) Dynamical localization in \(Z_2\) lattice gauge theories. Phys Rev B 97:245137. https://doi.org/10.1103/PhysRevB.97.245137

  8. Smith A, Knolle J, Kovrizhin DL, Moessner R (2017) Disorder-free localization. Phys Rev Lett 118:266601. https://doi.org/10.1103/PhysRevLett.118.266601

  9. Thouless DJ (1972) A relation between the density of states and range of localization for one dimensional random systems. J Phys C Solid State Phys 5:77–81. https://doi.org/10.1088/0022-3719/5/1/010

    Article  ADS  Google Scholar 

  10. Vardhan S, De Tomasi G, Heyl M, Heller EJ, Pollmann F (2017) Characterizing time irreversibility in disordered fermionic systems by the effect of local perturbations. Phys Rev Lett 119:016802. https://doi.org/10.1103/PhysRevLett.119.016802

  11. Antipov AE, Javanmard Y, Ribeiro P, Kirchner S (2016) Interaction-tuned anderson versus mott localization. Phys Rev Lett 117:146601. https://doi.org/10.1103/PhysRevLett.117.146601

  12. Alvermann A, Fehske H (2005) Local distribution approach to disordered binary alloys. Eur Phys J B 48:295–303. https://doi.org/10.1140/epjb/e2005-00408-8

    Article  ADS  Google Scholar 

  13. Janarek J, Delande D, Zakrzewski J (2018) Discrete disorder models for many-body localization. Phys Rev B 97:155133. https://doi.org/10.1103/PhysRevB.97.155133

  14. Aubry S, André G (1980) Analyticity breaking and anderson localization in incommensurate lattices. Ann Isreal Phys Soc 3:18

    MathSciNet  MATH  Google Scholar 

  15. Falicov LM, Kimball JC (1969) Simple model for semiconductor-metal transitions: SmB6 and transition-metal oxides. Phys Rev Lett 22:997–999. https://doi.org/10.1103/PhysRevLett.22.997

    Article  ADS  Google Scholar 

  16. Schubert G, Fehske H (2008) Dynamical aspects of two-dimensional quantum percolation. Phys Rev B 77:245130. https://doi.org/10.1103/PhysRevB.77.245130

  17. Schubert G, Fehske H (2009) Quantum percolation in disordered structures. arXiv:0905.2537

  18. Chandrashekar CM, Busch T (2015) Quantum percolation and transition point of a directed discrete-time quantum walk. Sci Rep 4:6583. https://doi.org/10.1038/srep06583

Download references

Author information

Authors and Affiliations

  1. Fakultät für Physik, Technische Universität München, Garching, Germany

    Dr. Adam Smith

Authors
  1. Dr. Adam Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adam Smith .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Smith, A. (2019). Localization. In: Disorder-Free Localization. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-20851-6_3

Download citation

Publish with us

Policies and ethics

Search

Navigation