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We study the set of infinite volume ground states of Kitaev's quantum double model on $\mathbb{Z}^2$ for an arbitrary finite abelian group $G$.
Haag, R., Hugenholtz, N.M., Winnink, M.: On the equilibrium states in quantum statistical mechanics . Commun. Math. Phys. 5
1967
Earlier work this paper cites.
Doplicher, S., Haag, R., Roberts, J.E.: Local observables and particle statistics. I . Commun. Math. Phys. 23
1971
Earlier work this paper cites.
Doplicher, S., Haag, R., Roberts, J.E.: Local observables and particle statistics. II . Commun. Math. Phys. 35
1974
Earlier work this paper cites.
Bratteli, O., Kishimoto, A., Robinson, D.: Ground states of infinite quantum spin systems . Commun. Math. Phys. 64
1978
Earlier work this paper cites.
Reed, M., Simon, B.: Methods of Modern Mathematical Physics Vol. I: Functional Analysis, Revised and Enlarged edition. Academic Press, 400 p. (1980)
1980
Earlier work this paper cites.
Arovas, D., Schrieffer, J.R., Wilczek, F.: Fractional statistics and the quantum Hall effect . Phys. Rev. Lett. 53
1984
Earlier work this paper cites.
Araki, H., Matsui, T.: Ground states of the X Y XY -model . Commun. Math. Phys. 101
1985
Earlier work this paper cites.
Bratteli, O., Robinson, D.W.: Operator algebras and quantum statistical mechanics 1 and 2, Second Edition. Springer Verlag (1987)
1987
Earlier work this paper cites.
Fredenhagen, K., Rehren, K.-H., Schroer, B.: Superselection sectors with braid group statistics and exchange algebras . Commun. Math. Phys. 125
1989
Earlier work this paper cites.
Wen, X.-G.: Vacuum degeneracy of chiral spin states in compactified space . Phys. Rev. Lett. B40
1989
Earlier work this paper cites.
Fröhlich, J., Gabbiani, F.: Braid statistics in local quantum theory . Rev. Math. Phys. 2
1990
Earlier work this paper cites.
Moore, G., Read, N.: Nonabelions in the fractional quantum Hall effect . Nucl. Phys. B 360
1990
Earlier work this paper cites.
1990
Earlier work this paper cites.
Dijkgraaf, R., Pasquier, V., Roche, P.: Quasi Hopf algebras, group cohomology and orbifold models . Nucl. Phys. B. Proc. Suppl. 18B
1991
Earlier work this paper cites.
Fannes, M., Nachtergaele, B., Werner, R. F.: Finitely correlated states of quantum spin chains . Commun. Math. Phys. 144
1992
Earlier work this paper cites.
Bais, F.A., van Driel, P., De Wild Propitius, M.: Anyons in discrete gauge theories with Chern-Simons terms . Nucl. Phys. B 393
1993
Earlier work this paper cites.
Szlachányi, K., Vecsernyés, P.: Quantum symmetry and braid group statistics in G G -spin models . Commun. Math. Phys. 156
1993
Earlier work this paper cites.
Fannes, M., Werner, R.F.: Boundary Conditions for Quantum Lattice Systems . Helv. Phys. Acta 68
1995
Cited alongside, same era.
Gottstein, C.T., Werner, R.F.: Ground states of the q q -deformed Heisenberg ferromagnet . arXiv:cond-mat/9501123 (1995)
1995
Cited alongside, same era.
Haag, R.: Local quantum physics: Fields, particles, algebras, Texts and Monographs in Physics. Springer-Verlag, Berlin, second edition (1996)
1996
Cited alongside, same era.
Matsui, T.: On ground states of the one-dimensional ferromagnetic XXZ chain . Lett. Math. Phys. 37
1996
Cited alongside, same era.
Bravyi, S., Kitaev, A.: Quantum codes on a lattice with boundary . arXiv:quant-ph/9811052v1 (1998)
1998
Cited alongside, same era.
Bonderson, P., Shtengel, K., Slingerland, J.K.: Interferometry of non-abelian anyons . Ann. Physics 323
2008
Later among the works it cites.
Beigi, S., Shor, P.W., Whalen, D.: The quantum double model with boundary: condensations and symmetries . Commun. Math. Phys. 306
2011
Later among the works it cites.
Bravyi, S., Hastings, M., Michalakis, S.: Topological quantum order: stability under local perturbations . J. Math. Phys. 51
2011
Later among the works it cites.
Chen, X., Gu, Z.-C., Wen, X.-G.: Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order , Phys. Rev. B 84
2011
Later among the works it cites.
Naaijkens, P.: Localized endomorphisms in Kitaev’s toric code on the plane . Rev. Math. Phys. 23
2011
Later among the works it cites.
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1998
Cited alongside, same era.
Koma, T., Nachtergaele, B.: The complete set of ground states of the ferromagnetic XXZ chains . Adv. Theor. Math. Phys. 2
1998
Cited alongside, same era.
Bakalov, B., Kirillov, Jr., A.: Lectures on Tensor Categories and Modular Functors (University Lecture Series 21). American Mathematical Society, Providence, RI (2001)
2001
Cited alongside, same era.
Freedman, M., Meyer, D.A.: Projective plane and planar quantum codes . Found. Comput. Math. 1
2001
Cited alongside, same era.
Kitaev, A.Y.: Fault-tolerant quantum computation by anyons . Ann. Physics 303
2003
Cited alongside, same era.
Hastings, M.B., Koma, T.: Spectral gap and exponential decay of correlations . Commun. Math. Phys. 265
2006
Cited alongside, same era.
Kitaev, A.: Anyons in an exactly solved model and beyond . Ann. Physics 321
2006
Cited alongside, same era.
Bachmann, S., Michalakis, S., Nachtergaele, B., Sims, R.: Automorphic equicalence within gapped phases of quantum lattice systems . Commun. Math. Phys. 309
2012
Later among the works it cites.
Michalakis, S., Zwolak, J.P: Stability of frustration-free Hamiltonians . Commun. Math. Phys. 322
2013
Later among the works it cites.
Bachmann, S., Ogata, Y.: C 1 C^{1} -classification of gapped parent Hamiltonians of quantum spin chains . Commun. Math. Phys. 338
2015
Later among the works it cites.
Brandão, F.G.S.L, Horodecki, M.: Exponential decay of correlations implies area law . Commun. Math. Phys. 333
2015
Later among the works it cites.
Fiedler, L., Naaijkens, P.: Haag duality for Kitaev’s quantum double model for abelian groups . Rev. Math. Phys. 27
2015
Later among the works it cites.
Naaijkens, P.: Kitaev’s quantum double model from a local quantum physics point of view . In: R. Brunetti C. Dappiaggi, K. Fredenhagen, J. Yngvason (eds.), Advances in Algebraic Quantum Field Theory, pp. 365–395. Springer (2015)
2015
Later among the works it cites.
2016
Closest in time.
Haah, J.: An invariant of topologically ordered states under local unitary transformations . Commun. Math. Phys. 342
2016
Closest in time.
Ogata, Y.: A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization I . Commun. Math. Phys. 348
2016
Closest in time.
Ogata, Y.: A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization II , Commun. Math. Phys. 348
2016
Closest in time.