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.
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.
Magic and entanglement are independent quantum resources, yet their exact relation in many-body dynamics has remained elusive. We uncover two structural principles. First, at any stabilizer state, the curvature of the second stabilizer Rényi entropy under an arbitrary Hermitian generator equals the quantum Fisher information up to a fixed normalization, creating a bidirectional bridge between computational and metrological resources. Second, for commuting Ising evolution on any forest graph, a Clifford pruning circuit yields the full stabilizer-Rényi family at arbitrary size and in any spatial embedding, thereby furnishing a graph-theoretic construction of families with finite magic density and vanishing entanglement density in the thermodynamic limit. We solve two paradigmatic one-dimensional realizations central to quantum simulation -- an Ising quench and a kicked Floquet chain -- exactly for arbitrary system size and directly in the thermodynamic limit, revealing finite magic density with vanishing entanglement density, distinct magic and entanglement revival periods, and Clifford points with zero magic but finite bipartite entanglement. The same tangent geometry fixes initial growth, perturbative revival lifting, and stability of thermodynamic magic minima. Large-scale Pauli-basis matrix-product-state calculations verify all predictions, and the tangent bridge yields a concrete protocol for detecting magic through established quantum-Fisher-information measurements.
Disorder-free quantum many-body localization can strongly suppress transport while still enabling the dynamical buildup of computationally costly non-Clifford resources. In a tilted transverse-field Ising chain realizing disorder-free Stark many-body localization, we use the stabilizer Rényi entropy to quantify quantum magic (nonstabilizerness) and find that it remains finite and grows anomalously slowly over extended time windows before saturating to a size-dependent plateau deep in the strong-tilt regime, with pronounced initial-state selectivity. Upon increasing the Stark gradient, the long-time magic and half-chain entanglement exhibit consistent finite-size crossing behavior, indicating a crossover from ergodic dynamics to constrained localization. These results establish stabilizer-based magic as a practical complexity diagnostic of disorder-free ergodicity breaking and constrained dynamics, and provide an experimentally accessible route to benchmarking and designing near-term quantum simulators.
Quantum magic, or non-stabilizerness, is an important quantum resource that characterizes computational power beyond classically simulable Clifford operations and is therefore essential for achieving quantum advantage. While previous studies have explored non-stabilizerness dynamics in random circuits and under time-independent generators, here we extend the study of its universal dynamics to time-dependent driving across quantum phase transitions. In particular, we show that the stabilizer Rényi entropies and the cumulants of the Pauli spectrum exhibit universal power-law scaling with the driving rate in slow processes. Moreover, we show that the logarithmic Pauli spectrum is asymptotically Gaussian, implying a lognormal distribution for the Pauli spectrum values. Our results are explicitly demonstrated by exact results in the transverse-field Ising model and by analytical approximations in long-range Kitaev models.
Stabilizer entropies and quantum magic have been extensively explored in real-space formulations of quantum systems within the framework of resource theory. However, interesting and transparent physics often emerges in momentum space, such as Cooper pairing. Motivated by this, we investigate the momentum-space structure of Pauli strings and stabilizer entropies in the one-dimensional transverse-field quantum Ising model. By mapping the Ising chain onto momentum-space qubits, where the stabilizer state corresponds to the paramagnetic state, we analyze the evolution of the Pauli string distribution. In the ferromagnetic phase, the distribution is broad, whereas in the paramagnetic phase, it develops a two-peaked structure. We demonstrate that all ferromagnetic states possess the same degree of magic in the thermodynamic limit, while stabilizer entropies are non-analytic at the critical point and vanish with increasing transverse field. The momentum-space approach to quantum magic not only complements its real-space counterpart but also provides advantages in terms of analyzing nonstabilizerness and classical simulability.
Magic, a quantum resource distinct from entanglement, measures departure from states stabilized by products of Pauli operators. Such stabilizer states can be maximally entangled yet admit efficient classical description: quantum advantage requires magic. We develop a powerful framework to evaluate the degree of magic in generic many-body states. We use it to study the fate of magic under thermal and dynamical evolution. In the transverse field Ising model, we find a thermal sudden death of magic that saturates with system size, and occurs after the death of entanglement. We reach similar conclusions in generic spin chains, and in the Kitaev quantum spin liquid on the honeycomb lattice, where the threshold shows an intricate dependence on subregion shape. We then study how magic equilibrates after a quantum quench. In quenches of generic spin chains, the magic of a subregion typically dies before entanglement, contrary to thermal trajectories. An explanation is given in terms of the geometry of non-magical states. As a third type of trajectory, we examine the fate of magic with separation with an appropriate notion of non-local magic and establish a sudden death. Finally, we show how to experimentally witness a volume law of frame-robust magic in quantum materials by using neutron scattering.
We investigate the quantum dynamics generated by quantum quenches (QQs) of the Hamiltonian parameters in many-body systems, focusing on protocols that cross first-order and continuous quantum transitions, both in finite-size systems and in the thermodynamic limit. As a paradigmatic example, we consider the quantum Ising chain in the presence of homogeneous transverse (g) and longitudinal (h) magnetic fields. This model exhibits a continuous quantum transition (CQT) at g=gc and h=0, and first-order quantum transitions (FOQTs) driven by h along the line h=0 (g<gc). In the integrable limit h=0, the system can be mapped onto a quadratic fermionic theory; however, any nonvanishing longitudinal field breaks integrability and the spectrum of the resulting Hamiltonian is generally expected to enter a chaotic regime. We analyze QQs in which the longitudinal field is suddenly changed from a negative value hi<0 to a positive value hf>0. We focus on values of hf such that the spectrum of the post-QQ Hamiltonian H(g,hf) lies in the chaotic regime, where thermalization may emerge at asymptotically long times. We study the out-of-equilibrium dynamics for different values of g, finding qualitatively distinct behaviors for g>gc (where the chain is in the disordered phase), for g=gc (QQ across the CQT), and for g<gc (QQ across the FOQT line).