Longitudinal-field suppression of quantum-magic backflow in an Ising chain

Abstract

Quantum quenches can generate substantial nonstabilizerness, but generating a large amount of magic does not by itself guarantee its later retention. We study an open transverse-field Ising chain perturbed by a longitudinal field that removes the free-fermion integrable structure of the G = 0 model. Exact finite-size calculations compare symmetry-resolved level statistics, stabilizer Rényi entropy, Pauli-spectrum memory, and a time-averaged magic-backflow measure. A weak longitudinal field increases the generated magic and suppresses large Pauli-spectrum revivals, while the field minimizing memory does not coincide with the largest finite-size adjacent-gap ratio. For the exact stabilizer state , a broad intermediate-field window strongly reduces magic backflow. At fixed and 0.12, this suppression remains approximately 80% through N = 11; extending the N = 11 evolution from to 32 leaves the suppression essentially unchanged. Pauli-spectrum revivals are reduced more modestly. Thus, the data establish a robust finite-size and finite-time separation between resource retention and Pauli-spectrum memory, without implying strict asymptotic irreversibility or a thermodynamic transition.