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 ℤ2 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.
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Acknowledgments
We deeply appreciate the long-term collaboration with Noa Feldman and Moshe Goldstein, which fruitfully influenced this project and the companion paper [94]. Discussions with Daniel Gonzalez-Cuadra, Yannick Meurice and Michael Smolkin are also greatfully acknowledged. We are grateful to the long term workshop YITP-T-23-01 held at YITP, Kyoto University, where a part of this work was done. JK is supported by the Israel Academy of Sciences and Humanities & Council for Higher Education Excellence Fellowship Program for International Postdoctoral Researchers.
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Knaute, J., Feuerstein, M. & Zohar, E. Entanglement and confinement in lattice gauge theory tensor networks. J. High Energ. Phys. 2024, 174 (2024). https://doi.org/10.1007/JHEP02(2024)174
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DOI: https://doi.org/10.1007/JHEP02(2024)174