Models for Gapped Boundaries and Domain Walls

Communications in Mathematical Physics

Volumn 313, Issue 2, 2012, Pages 351-373

  Kitaev, Alexei ^a   Kong, Liang ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84862844227     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-012-1500-5     Document Type: Article

References (35)

1. Bombin H.: Topological Order with a Twist: Ising Anyons from an Abelian Model. Phys. Rev. Lett. 105, 030403 (2010).
2. Bravyi, S. B., Kitaev, A. Y.: Quantum codes on a lattice with boundary. http://arxiv. org/abs/quant-ph/9811052v1, 1998.
3. Buerschaper, O., Mombelli, J. M., Christandl, M., Aguado, M.: A hierarchy of topological tensor network states. http://arxiv. org/abs/1007. 5283v1 [cond-mat-str-el], 2010.
4. Beigi S., Shor P., Whalen D.: The Quantum Double Model with Boundary: Condensations and Symmetries. Commun. Math. Phys. 306(3), 663-694 (2011).
5. Böhm G., Szlachányi K.: A coassociative C*-quantum group with nonintegral dimensions. Lett. Math. Phys. 35, 437-456 (1996).
6. Barrett J., Westbury B.: Invariants of piecewise-linear 3-manifolds. Trans. Amer. Math. Soc. 348(10), 3997-4022 (1996).
7. Deligne, P.: Catégories tannakiennes. The Grothendieck Festschrift, Vol. II, Progr. Math. 87, Boston, MA: Birkhäuser Boston, 1990, pp. 111-195.
8. Davydov A., Kong L., Runkel I.: Invertible defects and isomorphisms of rational CFTs. Adv. Theor. Math. Phys. 15, 43-69 (2011).
9. Etingof P., Nikshych D., Ostrik V.: On fusion categories. Ann. of Math. 162, 581-642 (2005).
10. Etingof P., Nikshych D., Ostrik V.: Weakly group-theoretical and solvable fusion categories. Adv. Math. 226(1), 176-205 (2010).
11. Etingof P., Nikshych D., Ostrik V.: Fusion categories and homotopy theory. Quantum Topol. 1(3), 209-273 (2010).
12. Etingof, P., Ostrik, V.: Finite tensor categories, Mosc. Math. J. 4(3), 627-654, 782-783 (2004).
13. Fröhlich J., Fuchs J., Runkel I., Schweigert C.: Duality and defects in rational conformal field theory. Nucl. Phys. B 763, 354-430 (2007).
14. Fröhlich J., Gabbiani F.: Braid statistics in local quantum field theory. Rev. Math. Phys. 2(3), 251-353 (1990).
15. Fredenhagen K., Rehren K. H., Schroer B.: Superselection sectors with braid group statistics and exchange algebras, I: General theory. Commun. Math. Phys. 125(2), 201-226 (1989).
16. Kapustin, A.: Topological Field Theory, Higher Categories, and Their Applications. In: Proceedings of the International Congress of Mathematicians, Vol. III. New Delhi: Hindustan Book Agency, 2010, pp. 2021-2043.
17. Kitaev A. Y.: Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2-30 (2003).
18. Kitaev A. Y.: Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2-111 (2006).
19. Kirillov, A. Jr., Balsam, B.: Turaev-Viro invariants as an extended TQFT. http://arxiv. org./abs/1004. 1533v3 [math. GT], 2010.
20. Kong, L.: In preparation.
21. Kapustin A., Saulina N.: Topological boundary conditions in abelian Chern-Simons theory. Nucl. Phys. B 845(3), 393-435 (2011).
22. Kapustin, A., Saulina, N.: Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory. In: Mathematical foundations of quantum field theory and perturbative string theory. Proc. Sympos. Pure Math., Vol. 83. Providence, RI: Amer. Math. Soc., 2011, pp. 175-198.
23. Kuperberg G.: Involutory Hopf algebras and 3-manifold invariants. Internat. J. Math. 2(1), 41-66 (1991).
24. Levin M. A., Wen X.-G.: String-net condensation: A physical mechanism for topological phases. Phys. Rev. B 71, 045110 (2005).
25. Lurie, J.: On the Classification of Topological Field Theories. In: Current developments in mathematics. Somerville, MA: Int. Press, 2009, pp. 129-280.
26. Mackaay M.: Spherical 2-categories and 4-manifold invariants. Adv. Math. 143, 288-348 (1999).
27. Misguich G., Serban D., Pasquier V.: Quantum Dimer Model on the Kagome Lattice: Solvable Dimer Liquid and Ising Gauge Theory. Phys. Rev. Lett. 89, 137202 (2002).
28. Moessner R., Sondhi S. L.: Resonating valence bond phase in the triangular lattice quantum dimer model. Phys. Rev. Lett. 86, 1881-1884 (2001).
29. Moore G., Read N.: Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360, 362-396 (1991).
30. Müger M.: From subfactors to categories and topology. I. Frobenius algebras in and Morita equivalence of tensor categories. J. Pure Appl. Algebra 180(1-2), 81-157 (2003).
31. Nikshych D.: Semisimple weak Hopf algebras. J. Algebra 275, 639-667 (2004).
32. Ostrik V.: Module categories, weak Hopf algebras and modular invariants. Transform. Groups 8(2), 177-206 (2003).
33. Read N., Chakraborty B.: Statistics of the excitations of the resonating-valence-bond state. Phys. Rev. B 40, 7133-7140 (1989).
34. Tambara D.: A duality for modules over monoidal categories of representations of semisimple Hopf algebras. J. Algebra 241, 515-547 (2001).
35. Turaev V. G., Viro O. Y.: State sum invariants of 3-manifolds and quantum 6j-symbol. Topology 31(4), 865-902 (1992).