Lecturer: Dr. Erez Zohar Affiliation: Max Planck Institute of Quantum Optics Abstract: Tensor networks, and in particular Projected Entangled Pair States (PEPS), are a powerful tool for the study of quantum many body physics, thanks to both their built-in ability of classifying and studying symmetries, and the efficient numerical calculations they allow. In the work I will present, we introduced a way to extend the set of symmetric PEPS in order to include local gauge invariance and investigate lattice gauge theories with fermionic matter [1]. I will review the basic ingredients of PEPS and the way of handling global symmetries with them, and show how to gauge them and make the symmetry local [2]. As an example, I will present our construction of fermionic PEPS, based on Gaussian schemes, invariant under both global and local U(1) gauge transformations. The obtained states describe a truncated U(1) lattice gauge theory [3] in 2+1 dimensions, involving both the gauge field and fermionic matter; I will present the methods which enabled us to study these states, and the results in which some well-known physical phases were identified (e.g. confinement of static charges and screening of dynamical ones). [1] Fermionic projected entangled pair states and local U(1) gauge theories, EZ, M. Burrello, T. B. Wahl and J. I. Cirac, Ann. Phys. 363, 385 (2015). [2] Building Projected Entangled Pair States with a Local Gauge Symmetry. EZ and M. Burrello, arxiv:1511.08426. [3] Formulation of lattice gauge theories for quantum simulations, EZ and M. Burrello, Phys. Rev. D 91, 054506 (2015). ‏האירוע הזה כולל שיחת וידאו ב-Google Hangouts. הצטרף: https://hangouts.google.com/hangouts/_/mail.huji.ac.il/condensed?hceid=b...