Reduced State Stabilizer Rényi Entropy as a Probe of Quantum Phase Transitions in Frustrated J1-J2 Spin Models

Quantum phase transitions occur at absolute zero temperature and are driven by quantum fluctuations. In frustrated quantum spin systems, such as models with competing nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions, conventional quantum correlation measures like bipartite entanglement often fail to signal ground-state phase transitions. This paper investigates whether nonstabilizerness, quantified through the stabilizer Rényi entropy (SRE), can serve as a reliable local indicator of quantum criticality in frustrated spin models where traditional diagnostics fall short.

The authors examine three paradigmatic frustrated spin models: the one-dimensional isotropic Heisenberg model, the one-dimensional anisotropic XXZ model, and the two-dimensional Heisenberg model on a 4x4 square lattice. Because real physical systems cannot be prepared at absolute zero, the study evaluates the purity-corrected SRE not only for the ground state but also for a low-temperature subjacent state. This subjacent state is modeled as a statistical mixture of the ground state and the lowest excited states using a Maxwell-Boltzmann-type occupation probability. To keep the computation tractable for larger systems, the SRE is evaluated locally on reduced two-qubit density matrices obtained by tracing out the rest of the lattice.

While single-site reduced density matrices yield a vanishing SRE due to global SU(2) symmetry, the two-qubit reduced density matrices retain short-range correlation information and successfully reveal critical behavior. For the one-dimensional isotropic model, the ground-state SRE exhibits a point of inflection while the subjacent-state SRE shows a discontinuity, yielding critical frustration parameters in excellent agreement with established values. For the one-dimensional XXZ model, the subjacent-state SRE successfully reproduces the full anisotropy-dependent phase diagram. Similarly, in the two-dimensional 4x4 model, the subjacent-state SRE clearly identifies multiple phase transitions corresponding to competing magnetic orders.