### Abstract

We discuss how to formulate lattice gauge theories in the tensor-network language. In this way, we obtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge theories and a tensor-network variational ansatz for gauge-invariant states that can be used in actual numerical computations. Our construction is also applied to the simplest realization of the quantum link models or gauge magnets and provides a clear way to understand their microscopic relation with the Kogut- Susskind lattice gauge theories. We also introduce a new set of gauge-invariant operators that modify continuously Rokhsar-Kivelson wave functions and can be used to extend the phase diagrams of known models. As an example, we characterize the transition between the deconfined phase of the Z2 lattice gauge theory and the Rokhsar-Kivelson point of the U(1) gauge magnet in 2D in terms of entanglement entropy. he topological entropy serves as an order parameter for the transition but not the Schmidt gap.

Original language | English |
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Article number | 041024 |

Number of pages | 29 |

Journal | Physical Review X |

Volume | 4 |

DOIs | |

Publication status | Published - 6 Nov 2014 |

### Keywords

- condensed matter physics
- particles and fields
- quantum physics

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## Cite this

Tagliacozzo, L., Celi, A., & Lewenstein, M. (2014). Tensor networks for lattice gauge theories with continuous groups.

*Physical Review X*,*4*, [041024]. https://doi.org/10.1103/PhysRevX.4.041024