## Internal Levin-Wen models

Vincentas Mulevičius, Ingo Runkel, Thomas Voß

SciPost Phys. 17, 088 (2024) · published 24 September 2024

- doi: 10.21468/SciPostPhys.17.3.088
- Submissions/Reports

### Abstract

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 $\mathcal{C}$.

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Vincentas Mulevičius, -
^{3}Ingo Runkel, -
^{3}Thomas Voß

^{1}Erwin Schrödinger International Institute for Mathematics and Physics [ESI]^{2}Vilniaus universitetas / Vilnius University^{3}Universität Hamburg / University of Hamburg [UH]