Reduced State Stabilizer Rényi Entropy as a Probe of Quantum Phase Transitions in Frustrated J_1-J_2 Spin Models

We investigate whether the second-order purity-corrected stabilizer Rényi entropy (SRE) of reduced two-qubit density matrices can serve as a reliable local indicator of quantum phase transitions (QPTs) in frustrated quantum spin systems. We consider the one-dimensional isotropic J₁-J₂ Heisenberg model, the one-dimensional XXZ J₁-J₂ model, and the two-dimensional J₁-J₂ Heisenberg model on a 4times4 square lattice. Unlike several previously studied quantum information measures, which fail to detect QPTs in the ground state of these frustrated systems, the reduced ground-state purity-corrected SRE successfully identifies most transitions. For the remaining cases, we consider a low temperature subjacent state, modeled as a statistical mixture of the ground and first excited states with a Maxwell--Boltzmann-type occupation probability. For the 1D isotropic model, the subjacent-state SRE shows a discontinuity at the critical point, yielding α_c\(infty=0.24116\), in excellent agreement with established values; the ground-state SRE shows a point of inflection, yielding α_c\(infty=0.2681\). For the 1D XXZ model, the subjacent-state SRE reproduces the full anisotropy dependent phase diagram, while the ground-state SRE captures transitions only at low anisotropy. For the 2D model, the subjacent-state SRE detects two transitions, at α_c\(4times4=0.40781\) and 0.6208, while the ground-state SRE identifies the second at 0.6230. Compared with conventional two-qubit entanglement, purity-corrected SRE shows a clear advantage in revealing otherwise-invisible phase transitions, establishing it as a robust, efficient, local probe of frustrated quantum criticality.