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arXiv · 2608.17313

Reduced State Stabilizer R\'enyi Entropy as a Probe of Quantum Phase Transitions in Frustrated J_1-J_2 Spin Models

George Biswas·Santanu Sarkar·Jun-Yi Wu·Anindya Biswas
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Abstract

We investigate whether the second-order purity-corrected stabilizer R\'enyi 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 \(J_1-J_2\) Heisenberg model, the one-dimensional XXZ \(J_1-J_2\) model, and the two-dimensional \(J_1-J_2\) Heisenberg model on a \(4\times4\) 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 \(\alpha_c(\infty)=0.24116\), in excellent agreement with established values; the ground-state SRE shows a point of inflection, yielding \(\alpha_c(\infty)=0.2681\). 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 \(\alpha_c(4\times4)=0.40781\) 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.

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George Biswas, Santanu Sarkar, Jun-Yi Wu, Anindya Biswas. 2026-08-18. Reduced State Stabilizer R\'enyi Entropy as a Probe of Quantum Phase Transitions in Frustrated J_1-J_2 Spin Models. https://arxiv.org/abs/2608.17313

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