Entanglement and confinement in lattice gauge theory tensor networks

Abstract

We develop a transfer operator approach for the calculation of Rényi entanglement entropies in arbitrary (i.e. Abelian and non-Abelian) pure lattice gauge theory projected entangled pair states in 2+1 dimensions. It is explicitly shown how the long-range behavior of these quantities gives rise to an entanglement area law in both the thermodynamic limit and in the continuum. We numerically demonstrate the applicability of our method to the $Z_2$ lattice gauge theory and relate some entanglement properties to the confinement-deconfinement transition therein. We provide evidence that Rényi entanglement entropies in certain cases do not provide a complete probe of (de)confinement properties compared to Wilson loop expectation values as other genuine (nonlocal) observables.

v2: minor extended discussions

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• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Duality transformations and the entanglement entropy of gauge theories
• Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach