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We construct an explicit renormalization group (RG) transformation for Levin and Wens string-net models on a hexagonal lattice. The transformation leaves invariant the ground-state fixed-point wave function of the string-net condensed phase. Our construction also produces an exact representation of the wave function in terms of the multi-scale entanglement renormalization ansatz (MERA). This sets the stage for efficient numerical simulations of string-net models using MERA algorithms. It also provides an explicit quantum circuit to prepare the string-net ground-state wave function using a quantum computer.
We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops expectation va
We describe how to construct generalized string-net models, a class of exactly solvable lattice models that realize a large family of 2D topologically ordered phases of matter. The ground states of these models can be thought of as superpositions of
Recently, a class of tensor networks called isometric tensor network states (isoTNS) was proposed which generalizes the canonical form of matrix product states to tensor networks in higher dimensions. While this ansatz allows for efficient numerical
We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. Firstly, we recall established techniques for how the partition function of a 2D classical man
We revisit a class of non-Hermitian topological models that are Galois conjugates of their Hermitian counter parts. Particularly, these are Galois conjugates of unitary string-net models. We demonstrate these models necessarily have real spectra, and