Abstract
Topological phases of matter remain a focus of interest due to their unique properties: fractionalization, ground-state degeneracy, and exotic excitations. While some of these properties can occur in systems of free fermions, their emergence is generally associated with interactions between particles. Here, we quantify the role of interactions in general classes of topological states of matter in one and two spatial dimensions, including parafermion chains and string-net models. Surprisingly, we find that certain topological states can be exactly described by free fermions, while others saturate the maximum possible distance from their optimal free-fermion description [C. J. Turner et al., Nat. Commun. 8, 14926 (2017)]. Our work opens the door to understanding the complexity of topological models by establishing new types of fermionization procedures to describe their low-energy physics, thus making them amenable to experimental realizations.
Highlights
A striking feature of many-body systems is their ability to exhibit collective phenomena without analog in their constituent particles
We have quantified the effect of interactions in the ground states of broad classes of topological phases of matter in all spatial dimensions
This analysis provides a clear picture of the landscape of renormalization group (RG) fixed-point models in terms of their free-fermion representation
Summary
A striking feature of many-body systems is their ability to exhibit collective phenomena without analog in their constituent particles. We consider parafermion chains [9], which are symmetry-protected topological phases, as well as twodimensional string nets [10,11], and Kitaev’s honeycomb lattice model [12] These models include renormalization group (RG) fixed points of general families of topological systems with excitations that exhibit anyonic and parafermionic statistics. We further demonstrate that families of Abelian string-net models have a ground state that can be expressed in terms of free fermions. This is highly counterintuitive as free-fermion models are typically not expected to support anyonic statistics. Extensive details and supplementary data are presented in the Appendix
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