Conformal field theories are magical
arXiv:2007.01303 · doi:10.1103/PhysRevB.103.075145
Abstract
"Magic" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the 3-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer, and constrain tensor network models of AdS-CFT.
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