Skip to main content

The Bilayer Double Semion Model

  • Chapter
  • First Online:
Topological Orders with Spins and Fermions

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

Abstract

An useful approach for studying topological orders in spin systems, especially those with interactions, is to construct exactly solvable models that realise them. Topological orders in spin systems are defined in a discrete lattice and a spin is located in each edge of the lattice.

¿Pero, y el espíritu libre? El venero de la inventiva. El terebrante husmeador de la realidad viva con ceñido escalpelo que penetra en lo que se agita y descubre allí algo que nunca vieron ojos no ibéricos. Como si fuera una lidia. Como si de cobaya a toro nada hubiera, como si todavía nosotros a pesar de la desesperación, a pesar de los créditos. Para los hombres como Amador, que ríen aunque están tristes, sabiendo que (...) nunca el investigador ante el rey alto recibirá la copa, el laurel, una antorcha encendida con que correr ante la tribuna de las naciones y proclamar la grandeza no sospechada que el pueblo de aquí obtiene en la lidia (...).

— L. Martín Santos, Tiempo de silencio (1962)

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

Access this chapter

eBook
USD 16.99
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. Kitaev AYu (2003) Fault-tolerant quantum computation by anyons. Ann Phys 303(1):2–30

    Google Scholar 

  2. Mesaros A, Ran Y (2013) Classification of symmetry enriched topological phases with exactly solvable models. Phys Rev B 87:155115

    Google Scholar 

  3. Jiang S, Ran Y (2015) Symmetric tensor networks and practical simulation algorithms to sharply identify classes of quantum phases distinguishable by short-range physics. Phys Rev B 92:104414

    Article  ADS  Google Scholar 

  4. Hermele M (2014) String flux mechanism for fractionalization in topologically ordered phases. Phys Rev B 90:184418

    Article  ADS  Google Scholar 

  5. Essin AM, Hermele M (2013) Classifying fractionalization: symmetry classification of gapped \({\mathbb{Z}}_{2}\) spin liquids in two dimensions. Phys Rev B 87:104406

    Google Scholar 

  6. Song H, Hermele M (2015) Space-group symmetry fractionalization in a family of exactly solvable models with \({\mathbb{Z}}_{2}\) topological order. Phys Rev B 91:014405

    Article  ADS  Google Scholar 

  7. Levin M, Gu Z-C (2012) Braiding statistics approach to symmetry-protected topological phases. Phys Rev B 86:115109

    Google Scholar 

  8. von Keyserlingk CW, Burnell FJ, Simon SH (2013) Three-dimensional topological lattice models with surface anyons. Phys Rev B 87:045107

    Google Scholar 

  9. Ortiz L, Martin-Delgado MA (2016) A bilayer double semion model with symmetry-enriched topological order. Ann Phys 375:193–226

    Article  ADS  MathSciNet  Google Scholar 

  10. Levin MA, Wen X-G (2005) String-net condensation: a physical mechanism for topological phases. Phys Rev B 71:045110

    Google Scholar 

  11. Chen X, Gu Z-C, Liu Z-X, Wen X-G (2013) Symmetry protected topological orders and the group cohomology of their symmetry group. Phys Rev B 87:155114

    Google Scholar 

  12. Bombin H (2010) Topological order with a twist: ising anyons from an abelian model. Phys Rev Lett 105:030403

    Google Scholar 

  13. Barkeshli M, Jian C-M, Qi X-L (2013) Theory of defects in abelian topological states. Phys Rev B 88:235103

    Article  ADS  Google Scholar 

  14. Tarantino N, Lindner NH, Fidkowski L (2016) Symmetry fractionalization and twist defects. New J Phys 18(3):035006

    Article  MathSciNet  Google Scholar 

  15. Yoshida B (2015) Topological color code and symmetry-protected topological phases. Phys Rev B 91:245131

    Article  ADS  Google Scholar 

  16. Beni Y (2016) Topological phases with generalized global symmetries. Phys Rev B 93:155131

    Article  Google Scholar 

  17. Terhal BM (2015) Quantum error correction for quantum memories. Rev Mod Phys 87:307–346

    Article  ADS  MathSciNet  Google Scholar 

  18. Brell CG (2015) Generalized color codes supporting non-abelian anyons. Phys Rev A 91:042333

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Laura Ortiz Martín .

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

Martín, L. (2019). The Bilayer Double Semion Model. In: Topological Orders with Spins and Fermions. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-23649-6_3

Download citation

Publish with us

Policies and ethics