Condensate-induced transitions between topologically ordered phases

By F. Bais, Joost Slingerland. 2008

238 citations recorded by the source corpus.

We investigate transitions between topologically ordered phases in two spatial dimensions induced by the condensation of a bosonic quasiparticle. To this end, we formulate an extension of the theory of symmetry-breaking phase transitions which applies to phases with topological excitations described by quantum groups or modular tensor categories. This enables us to deal with phases whose quasiparticles have noninteger quantum dimensions and obey braid statistics. Many examples of such phases can be constructed from two-dimensional rational conformal field theories, and we find that there is a beautiful connection between quantum group symmetry breaking and certain well-known constructions in conformal field theory, notably the coset construction, the construction of orbifold models, and more general conformal extensions. Besides the general framework, many representative examples are worked out in detail.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/2f88584f1be253857f02ab0d478a032df4ba937c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. J. Alicea
2. N. Lindner
3. A. Stern
4. C. Nayak
5. Po-Shen Hsin
6. P. Fendley
7. Ho Tat Lam
8. Roger S. K. Mong

In Condensed Matter Physics

1. Po-Shen Hsin
2. J. Alicea
3. Ho Tat Lam
4. Roger S. K. Mong
5. A. Stern
6. C. Nayak
7. Matthew Fisher
8. Liang Kong

Citations in the corpus

• Comments on one-form global symmetries and their gauging in 3d and 4d (2018, background): “up by a subgroup of the center [11,1]. In the condensed matter literature, it is called \anyon condensation" of the Abelian anyon that corresponds to the generating line of the one-form symmetry [13]. For p= 0 when the symmetry generating line ahas integer spin the gauging involves three steps ”
• Anyon condensation and tensor categories (2013, background): “ould relates to some mathematical structures in modular tensor categories. Although there are many works on anyon condensation by physicists, in particular the influential work of Bais and Slingerland [BS] (see also forexample [BM-D][BW] and references therein), the fundamental mathematical structure”
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure (2013, methodology): “The properties of this “broken SUð2Þ4” theory [160], including the confined ~ X excitation, appear in Table III.”
• The continuum limit of loop quantum gravity - a framework for solving the theory (2014, background): “In particular the notion of dynamical embedding maps and related vacua states describe condensation phenomena – in the 2D intertwiner models of anyons described by SU(2)k fusion modules [42, 43].”