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We introduce a method to measure many-body magic in quantum systems based ona statistical exploration of Pauli strings via Markov chains. We demonstratethat sampling such Pauli-Markov chains gives ample flexibility in terms ofpartitions where to sample from: in particular, it enables to efficientlyextract the magic contained in the correlations between widely-separatedsubsystems, which characterizes the nonlocality of magic. Our method can beimplemented in a variety of situations. We describe an efficient samplingprocedure using Tree Tensor Networks, that exploits their hierarchicalstructure leading to a modest $O(\log N)$ computational scaling with systemsize. To showcase the applicability and efficiency of our method, wedemonstrate the importance of magic in many-body systems via the followingdiscoveries: (a) for one dimensional systems, we show that long-range magicdisplays strong signatures of conformal quantum criticality (Ising, Potts, andGaussian), overcoming the limitations of full state magic; (b) intwo-dimensional $\mathbb{Z}_2$ lattice gauge theories, we provide conclusiveevidence that magic is able to identify the confinement-deconfinementtransition, and displays critical scaling behavior even at relatively modestvolumes. Finally, we discuss an experimental implementation of the method,which only relies on measurements of Pauli observables.

Many-body magic via Pauli-Markov chains -- from criticality to gauge theories