Tensor Networks: an Overview

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Tensor network algorithms provide highly competitive tools for analyzing ground state properties of quantum lattice models in one and two spatial dimensions. The most notable examples involve matrix product states, projected entangled pair states and multiscale entanglement renormalization ansatz. The key underlying idea of all the approaches is to decompose a quantum many-body state into a carefully chosen network of tensors.
In this talk I will give an introduction to the subject and show how tensor networks can be used to characterize topological order.