Citation: Freedman, Michael, et al. "A class of P, T-invariant topological phases of interacting electrons." Annals of Physics 310.2 (2004): 428-492.
Web: https://arxiv.org/abs/cond-mat/0307511
Tags: Foundational, Temperley-Lieb, Abelian-anyons, TQFT, Quantum-groups
This paper introduces a family of topological phases of matter corresponding to doubled SU(2)_k quantum group models. This is done from the Chern-Simons theory. The authors use the Chern-Simons theory QFT formalism to derive a loop algebra for excitations, which gives a graphical calculus for determining braiding and fusion rules. The graphical language for describing doubled SU(2)_k is shown to be exactly the same as the graphical language of the k-strand Temperley-Lieb algebra.
One of the big takeaways from this paper is the loop algebra method of determining the properties of quasiparticles. It has since become a staple of the field, and is a standard way of thinking about topological order. It emphasizes that standard CFT methods like Chern-Simons theory can be connected anyon diagrammatics in special cases without going through general machinery such as Turaev-Viro TQFT.
One interesting feature of this paper is that despite having strong control of the properties of these doubled phases, the authors are not able to construct explicit lattice Hamiltonians to realize the phases. Deriving such a Hamiltonian had to wait until
> Freedman, Michael, Chetan Nayak, and Kirill Shtengel. "Non-Abelian topological phases in an extended Hubbard model." arXiv preprint cond-mat/0309120 (2003).
Nowadays, we would simply view the Hamiltonian as a special case of the Levin-Wen model.
This paper is amazingly physically minded and physically grounded. It touches on a large number of very interesting topics. At times this can make it hard to read, but it is very much worth it.