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H.-J. Schmiedmayer:
"QFTs emerging from many-body quantum physics";
Keynote Lecture: Pollica Summer Workshop, Pollica Italien (invited); 2022-06-20 - 2022-07-01.

Quantum Field theories are a natural way to describe quantum many body systems. Irrelevant details of the microscopic physics are ignored and new relevant degrees of freedom, described by the QFT, emerge at a larger scale. I will illustrate this in the example of the emergence of the Sine-Gordon quantum field theory from the microscopic description of two tunnel coupled super fluids [1] and in the emergence of Pauli blocking in a weakly interacting Bose gas [2]. Special emphasis will be put on how to verify such emergent quantum simulators and how to characterize them. Thereby I will present two tools: High order correlation functions and their factorization [1], the evaluation of the quantum effective action and the momentum dependence of propagators and vertices (running couplings, renormalization of mass etc ..) of the emerging quantum field theory [3] and quantum field tomography that points to a new way to read out quantum simulators [4]. Together they establish general methods to analyse quantum systems through experiments and thus represents a crucial ingredient towards the implementation and verification of quantum simulators. As an example, I will report on the progress towards measuring area laws of mutual information and entanglement entropy in a QFT, and the study of information fronts in curved space time.