TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.3.088
TI  - Internal Levin-Wen models
PY  - 2024/09/24
UR  - https://scipost.org/SciPostPhys.17.3.088
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 3
SP  - 088
A1  - Mulevičius, Vincentas
AU  - Runkel, Ingo
AU  - Voß, Thomas
AB  - Levin--Wen models are a class of two-dimensional lattice spin models with a Hamiltonian that is a sum of commuting projectors, which describe topological phases of matter related to Drinfeld centres. We generalise this construction to lattice systems internal to a topological phase described by an arbitrary modular fusion category $\mathcal{C}$. The lattice system is defined in terms of an orbifold datum $\mathbb{A}$ in $\mathcal{C}$, from which we construct a state space and a commuting-projector Hamiltonian $H_{\mathbb{A}}$ acting on it. The topological phase of the degenerate ground states of $H_{\mathbb{A}}$ is characterised by a modular fusion category $\mathcal{C}_\mathbb{A}$ defined directly in terms of $\mathbb{A}$. By choosing different $\mathbb{A}$'s for a fixed $\mathcal{C}$, one obtains precisely all phases which are Witt-equivalent to $\mathcal{C}$. As special cases we recover the Kitaev and the Levin--Wen lattice models from instances of orbifold data in the trivial modular fusion category of vector spaces, as well as phases obtained by anyon condensation in a given phase $\mathcal{C}$.
ER  -

@Article{10.21468/SciPostPhys.17.3.088,
	title={{Internal Levin-Wen models}},
	author={Vincentas Mulevičius and Ingo Runkel and Thomas Voß},
	journal={SciPost Phys.},
	volume={17},
	pages={088},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.3.088},
	url={https://scipost.org/10.21468/SciPostPhys.17.3.088},
}