Skip to main content

The Model

  • Chapter
  • First Online:
Disorder-Free Localization

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

  • 366 Accesses

Abstract

The main contribution of this thesis is the introduction of a family of models that have a disorder-free mechanism for localization. In this chapter we define the models and reveal an exact mapping to free fermions using a local \(\mathbb {Z}_2\) gauge symmetry. This mapping unveils the mechanism for localization and allows us to perform efficient large-scale numerical simulations to demonstrate the localization behaviour, which we do in the subsequent chapters.

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

Access this chapter

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

Institutional subscriptions

References

  1. Fradkin E (2013) Field theories of condensed matter physics. Cambridge University Press, Cambridge, UK. https://doi.org/10.1017/CBO9781139015509

  2. Essler FHL, Frahm H, Göhman F, Klümper A, Korepin VE (2005) The one-dimensional Hubbard model. Cambridge University Press, Cambridge, UK

    Book  Google Scholar 

  3. 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 

  4. Kitaev AY (2003) Fault-tolerant quantum computation by anyons. Ann Phys (NY) 303:2–30. https://doi.org/10.1016/S0003-4916(02)00018-0

    Article  ADS  MathSciNet  Google Scholar 

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

  6. Kogut JB (1979) An introduction to lattice gauge theory and spin systems. Rev Mod Phys 51:659–713. https://doi.org/10.1103/RevModPhys.51.659

    Article  ADS  MathSciNet  Google Scholar 

  7. Wen X-G (2007) Quantum field theory of many-body systems. Oxford University Press, Oxford, UK. https://doi.org/10.1093/acprof:oso/9780199227259.001.0001

  8. Kitaev AY (2006) Anyons in an exactly solved model and beyond. Ann Phys (NY) 321:2–111. https://doi.org/10.1016/j.aop.2005.10.005

    Article  ADS  MathSciNet  Google Scholar 

  9. Prosko C, Lee S-P, Maciejko J (2017) Simple \(Z_2\) gauge theories at finite fermion density. Phys Rev B 96:205104. https://doi.org/10.1103/PhysRevB.96.205104

  10. Paredes B, Verstraete F, Cirac JI (2005) Exploiting quantum parallelism to simulate quantum random many-body systems. Phys Rev Lett 95:140501. https://doi.org/10.1103/PhysRevLett.95.140501

  11. Gogolin AO, Nersesyan AA, Tsvelik AM (1998) Bosonization and strongly correlated systems. Cambridge University Press, Cambridge, UK

    Google Scholar 

  12. Baskaran G, Mandal S, Shankar R (2007) Exact results for spin dynamics and fractionalization in the Kitaev model. Phys Rev Lett 98:247201. https://doi.org/10.1103/PhysRevLett.98.247201

  13. Knolle J, Kovrizhin DL, Chalker JT, Moessner R (2014) Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes. Phys Rev Lett 112:207203. http://journals.aps.org/prl/supplemental/10.1103/PhysRevLett.112.207203

  14. Ashcroft NW, Mermin ND (1976) Solid state physics. Cengage Learning

    Google Scholar 

  15. Rüegg A, Huber SD, Sigrist M (2010) Z2-slave-spin theory for strongly correlated fermions. Phys Rev B 81:155118. https://doi.org/10.1103/PhysRevB.81.155118

  16. Žitko R, Fabrizio M (2015) Z2 gauge theory description of the Mott transition in infinite dimensions. Phys Rev B 91:245130. https://doi.org/10.1103/PhysRevB.91.245130

  17. 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

  18. Herrmann AJ, Antipov AE, Werner P (2018) Spreading of correlations in the Falicov-Kimball model. Phys Rev B 97:165107. https://doi.org/10.1103/PhysRevB.97.165107

  19. Gazit S, Randeria M, Vishwanath A (2017) Emergent Dirac fermions and broken symmetries in confined and deconfined phases of Z2 gauge theories. Nat Phys 13:484–490. https://doi.org/10.1038/nphys4028

    Article  ADS  Google Scholar 

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

  21. Smith A, Knolle J, Moessner R, Kovrizhin DL (2017b) Absence of ergodicity without quenched disorder: from quantum disentangled liquids to many-body localization. Phys Rev Lett 119:176601. https://doi.org/10.1103/PhysRevLett.119.176601

  22. Brenes M, Dalmonte M, Heyl M, Scardicchio A (2018) Many-body localization dynamics from gauge invariance. Phys Rev Lett 120:030601. https://doi.org/10.1103/PhysRevLett.120.030601

Download references

Author information

Authors and Affiliations

Authors

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). The Model. In: Disorder-Free Localization. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-20851-6_2

Download citation

Publish with us

Policies and ethics