Citation: Wen, Xiao-Gang, and Qian Niu. "Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces." Physical Review B 41.13 (1990): 9377.
Web: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.41.9377
Tags: Foundational, Quantum-hall-effect, Physical, TQFT
This is the paper which first showed that topological order has a stable degeneracy on high genus surfaces, thus establishing one of the key phenomena people use to characterize topological order. The authors write about this as follows: "The ground-state degeneracy of the FQH states has been a puzzling problem for a long time. Especially, it is not clear whether the degeneracy arises from broken symmetries or not. There are arguments both favoring and disfavoring the symmetry-breaking picture". This paper argues that since the degeneracy on a Riemann surface is invariant under arbitrary noise which could break any symmetry, the degeneracy cannot be due to symmetry breaking! Thus, this is the paper which "breaks" Landau theory.
Another lovely touch about this paper is the following comment: "The ground-state degeneracy of the FQH states has been a puzzling problem for a long time. Especially, it is not clear whether the degeneracy arises from broken symmetries or not. There are arguments both favoring and disfavoring the symmetry-breaking picture". This sort of generalized Landau paradigm has thus been present ever since the Landau paradigm was first broken! It is now a very vogue topic, see e.g.
> McGreevy, John. "Generalized symmetries in condensed matter." Annual Review of Condensed Matter Physics 14.1 (2023): 57-82.