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 espÃritu 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 allà algo que nunca vieron ojos no ibéricos. Como si fuera una lidia. Como si de cobaya a toro nada hubiera, como si todavÃa nosotros a pesar de la desesperación, a pesar de los créditos. Para los hombres como Amador, que rÃen 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 aquà obtiene en la lidia (...).
— L. MartÃn Santos, Tiempo de silencio (1962)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kitaev AYu (2003) Fault-tolerant quantum computation by anyons. Ann Phys 303(1):2–30
Mesaros A, Ran Y (2013) Classification of symmetry enriched topological phases with exactly solvable models. Phys Rev B 87:155115
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
Hermele M (2014) String flux mechanism for fractionalization in topologically ordered phases. Phys Rev B 90:184418
Essin AM, Hermele M (2013) Classifying fractionalization: symmetry classification of gapped \({\mathbb{Z}}_{2}\) spin liquids in two dimensions. Phys Rev B 87:104406
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
Levin M, Gu Z-C (2012) Braiding statistics approach to symmetry-protected topological phases. Phys Rev B 86:115109
von Keyserlingk CW, Burnell FJ, Simon SH (2013) Three-dimensional topological lattice models with surface anyons. Phys Rev B 87:045107
Ortiz L, Martin-Delgado MA (2016) A bilayer double semion model with symmetry-enriched topological order. Ann Phys 375:193–226
Levin MA, Wen X-G (2005) String-net condensation: a physical mechanism for topological phases. Phys Rev B 71:045110
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
Bombin H (2010) Topological order with a twist: ising anyons from an abelian model. Phys Rev Lett 105:030403
Barkeshli M, Jian C-M, Qi X-L (2013) Theory of defects in abelian topological states. Phys Rev B 88:235103
Tarantino N, Lindner NH, Fidkowski L (2016) Symmetry fractionalization and twist defects. New J Phys 18(3):035006
Yoshida B (2015) Topological color code and symmetry-protected topological phases. Phys Rev B 91:245131
Beni Y (2016) Topological phases with generalized global symmetries. Phys Rev B 93:155131
Terhal BM (2015) Quantum error correction for quantum memories. Rev Mod Phys 87:307–346
Brell CG (2015) Generalized color codes supporting non-abelian anyons. Phys Rev A 91:042333
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
MartÃn, 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
DOI: https://doi.org/10.1007/978-3-030-23649-6_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-23648-9
Online ISBN: 978-3-030-23649-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)