"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 Z3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q=3 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.

1 aWhite, Christopher, David1 aCao, ChunJun1 aSwingle, Brian uhttps://arxiv.org/abs/2007.0130301733nas a2200133 4500008004100000245014300041210006900184260001400253520122700267100001601494700003001510700002201540856003701562 2021 eng d00aLocalization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain0 aLocalization crossover and subdiffusive transport in a classical c9/22/20213 aWe consider the random-field Heisenberg model, a paradigmatic model for many-body localization (MBL), and add a Markovian dephasing bath coupled to the Anderson orbitals of the model's non-interacting limit. We map this system to a classical facilitated hopping model that is computationally tractable for large system sizes, and investigate its dynamics. The classical model exhibits a robust crossover between an ergodic (thermal) phase and a frozen (localized) phase. The frozen phase is destabilized by thermal subregions (bubbles), which thermalize surrounding sites by providing a fluctuating interaction energy and so enable off-resonance particle transport. Investigating steady state transport, we observe that the interplay between thermal and frozen bubbles leads to a clear transition between diffusive and subdiffusive regimes. This phenomenology both describes the MBL system coupled to a bath, and provides a classical analogue for the many-body localization transition in the corresponding quantum model, in that the classical model displays long local memory times. It also highlights the importance of the details of the bath coupling in studies of MBL systems coupled to thermal environments.

1 aKlocke, Kai1 aWhite, Christopher, David1 aBuchhold, Michael uhttps://arxiv.org/abs/2109.10926