2000 character limit reached
Topological and nontopological degeneracies in generalized string-net models
Published 1 Sep 2023 in cond-mat.other and quant-ph | (2309.00343v4)
Abstract: Generalized string-net models have been recently proposed in order to enlarge the set of possible topological quantum phases emerging from the original string-net construction. In the present work, we do not consider vertex excitations and restrict to plaquette excitations, or fluxons, that satisfy important identities. We explain how to compute the energy-level degeneracies of the generalized string-net Hamiltonian associated to an arbitrary unitary fusion category. In contrast to the degeneracy of the ground state, which is purely topological, that of excited energy levels depends not only on the Drinfeld center of the category, but also on internal multiplicities obtained from the tube algebra defined from the category. For a noncommutative category, these internal multiplicities result in extra nontopological degeneracies. Our results are valid for any trivalent graph and any orientable surface. We illustrate our findings with nontrivial examples.
- J. M. Leinaas and J. Myrheim, On the theory of identical particles, Il Nuovo Cimento B 37, 1 (1977).
- F. Wilczek, Quantum mechanics of fractional-spin particles, Phys. Rev. Lett. 49, 957 (1982).
- G. AI, Observation of non-Abelian exchange statistics on a superconducting processor, arXiv:2210.10255.
- A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. (NY) 303, 2 (2003).
- M. A. Levin and X.-G. Wen, String-net condensation: A physical mechanism for topological phases, Phys. Rev. B 71, 045110 (2005).
- C.-H. Lin and M. Levin, Generalizations and limitations of string-net models, Phys. Rev. B 89, 195130 (2014).
- T. Lan and X.-G. Wen, Topological quasiparticles and the holographic bulk-edge relation in (2+1)21(2+1)( 2 + 1 )-dimensional string-net models, Phys. Rev. B 90, 115119 (2014).
- A. Hahn and R. Wolf, Generalized string-net model for unitary fusion categories without tetrahedral symmetry, Phys. Rev. B 102, 115154 (2020).
- C.-H. Lin, M. Levin, and F. J. Burnell, Generalized string-net models: A thorough exposition, Phys. Rev. B 103, 195155 (2021).
- A. Kirillov, String-net model of Turaev-Viro invariants, arXiv:1106.6033.
- Y. Hu, N. Geer, and Y.-S. Wu, Full dyon excitation spectrum in extended Levin-Wen models, Phys. Rev. B 97, 195154 (2018).
- G. Moore and N. Seiberg, Classical and quantum conformal field theory, Commun. Math. Phys. 123, 177 (1989).
- E. Verlinde, Fusion rules and modular transformations in 2D conformal field theory, Nucl. Phys. B 300, 360 (1988).
- O. Buerschaper and M. Aguado, Mapping Kitaev’s quantum double lattice models to Levin and Wen’s string-net models, Phys. Rev. B 80, 155136 (2009).
- S. H. Simon, Topological Quantum (Oxford University Press, Oxford, 2023).
- M. Asaeda and U. Haagerup, Exotic Subfactors of Finite Depth with Jones Indices (5+13)/25132(5+\sqrt{13})/2( 5 + square-root start_ARG 13 end_ARG ) / 2 and (5+17)/25172(5+\sqrt{17})/2( 5 + square-root start_ARG 17 end_ARG ) / 2, Commun. Math. Phys. 202, 1 (1999).
- S.-M. Hong, E. Rowell, and Z. Wang, On exotic modular categories, Commun. Contemp. Math. 10, 1049 (2008).
- J. Vidal, Partition function of the Levin-Wen model, Phys. Rev. B 105, L041110 (2022).
- M. D. Schulz, S. Dusuel, and J. Vidal, Russian doll spectrum in a non-Abelian string-net ladder, Phys. Rev. B 91, 155110 (2015).
- Y. Hu, S. D. Stirling, and Y.-S. Wu, Ground-state degeneracy in the Levin-Wen model for topological phases, Phys. Rev. B 85, 075107 (2012).
- Y. Hu, S. D. Stirling, and Y.-S. Wu, Emergent exclusion statistics of quasiparticles in two-dimensional topological phases, Phys. Rev. B 89, 115133 (2014).
- A. Ocneanu, Operator Algebras, Topology and Subgroups of Quantum Symmetry —Construction of Subgroups of Quantum Groups—, Adv. Stud. Pure Math. 31, 235 (2001).
- AnyonWiki.
- A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. (NY) 321, 2 (2006).
- D. Tambara and S. Yamagami, Tensor categories with fusion rules of self-duality for finite abelian groups, J. Algebra 209, 692 (1998).
- V. Pasquier, Operator content of the ADE lattice models, J. Phys. A 20, 5707 (1987).
- C. L. Kane and M. P. A. Fisher, Quantized thermal transport in the fractional quantum Hall effect, Phys. Rev. B 55, 15832 (1997).
- A. Kitaev and L. Kong, Models for gapped boundaries and domain walls, Commun. Math. Phys. 313, 351 (2012).
- L. Kong, Anyon condensation and tensor categories, Nucl. Phys. B 886, 436 (2014).
- M. A. Levin, Protected Edge Modes without Symmetry, Phys. Rev. X 3, 021009 (2013).
- S. H. Simon and P. Fendley, Exactly solvable lattice models with crossing symmetry, J. Phys. A 46, 105002 (2013).
- M. Hermanns and S. Trebst, Renyi entropies for classical string-net models, Phys. Rev. B 89, 205107 (2014).
- M. Müger, From subfactors to categories and topology II: The quantum double of tensor categories and subfactors, J. Pure Appl. Algebra 180, 159 (2003).
- J. Slingerland, private communication.
- S. Beigi, P. W. Shor, and D. Whalen, The Quantum Double Model with Boundary: Condensations and Symmetries, Commun. Math. Phys. 306, 663 (2011).
- L. Lootens, C. Delcamp, and F. Verstraete, Dualities in one-dimensional quantum lattice models: topological sectors, arXiv:2211.03777.
- F. A. Bais and J. K. Slingerland, Condensate-induced transitions between topologically ordered phases, Phys. Rev. B 79, 045316 (2009).
- Y. Kawahigashi, A remark on gapped domain walls between topological phases, Lett. Math. Phys. 105, 893 (2015).
- I. Cong, M. Cheng, and Z. Wang, Topological Quantum Computation with Gapped Boundaries,arXiv:1609.02037.
- P. Grossman and N. Snyder, Quantum Subgroups of the Haagerup Fusion Categories, Commun. Math. Phys. 311, 617 (2012).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
