Non-stabilizerness versus entanglement in matrix product states

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In this paper, we investigate the relationship between entanglement and non-stabilizerness (also known as magic) in matrix product states (MPSs).

• We study the relation between magic and the bond dimension used to approximate the ground state of a many-body system in two different contexts: full state of magic and mutual magic (the non-stabilizer analogue of mutual information, thus free of boundary effects) of spin-1 anisotropic Heisenberg chains.
• Our results indicate that obtaining converged results for non-stabilizerness is typically considerably easier than entanglement.
• For full state magic at critical points and at sufficiently large volumes, we observe convergence with $1/\chi^2$, with $\chi$ being the MPS bond dimension.