Complexity of frustration: a new source of non-local non-stabilizerness

Understand

We advance the characterization of complexity in quantum many-body systems by examining $W$-states embedded in a spin chain.

• Such states show an amount of non-stabilizerness or "magic" (measured as the Stabilizer R\'enyi Entropy -SRE-) that grows logarithmic with the number of qubits/spins.
• We focus on systems whose Hamiltonian admits a classical point with an extensive degeneracy.
• Near these points, a Clifford circuit can convert the ground state into a $W$-state, while in the rest of the phase to which the classic point belongs, it is dressed with local quantum correlations.