Reduced-State Stabilizer R\'enyi Entropy as a Probe of Quantum Criticality in the Transverse ANNNI Model and the Quantum Compass Model

TL;DR

This study demonstrates that stabilizer R'enyi entropy of reduced states effectively detects quantum phase transitions in spin models, highlighting the role of non-stabilizer resources in quantum criticality.

Contribution

It shows the utility of purity-corrected stabilizer R'enyi entropy as a probe for quantum phase transitions in the transverse ANNNI and quantum compass models.

Findings

Purity-corrected SRE detects the antiphase--floating phase transition in TANNNI.

Raw SRE accurately reproduces ferromagnetic--paramagnetic boundaries in TANNNI.

Purity-corrected SRE signals the first-order transition at the isotropic point in QCM.

Abstract

We investigate the effectiveness of the stabilizer R\'enyi entropy (SRE), a quantifier associated with non-stabilizer resources (quantum magic), as an indicator of quantum phase transitions. Specifically, we analyze the behavior of the purity-corrected SRE of reduced density matrices in the ground states of two one-dimensional spin models: the transverse axial next-nearest-neighbor Ising (TANNNI) model and the quantum compass model (QCM). The ground state of the TANNNI model is obtained using exact diagonalization techniques, while the QCM is analyzed using the Jordan--Wigner (JW) transformation followed by Bogoliubov diagonalization of the resulting quadratic fermionic Hamiltonian. For the TANNNI model, the purity-corrected SRE successfully detects the antiphase--floating phase transition in the high-frustration regime, while in the low-frustration regime the raw (purity-uncorrected) SRE reproduces the known ferromagnetic--paramagnetic phase boundaries more accurately. For the QCM, the purity-corrected SRE exhibits a clear signature near the isotropic point \(J_x/J_z=1\), where the system undergoes a first-order quantum phase transition. Our results establish SRE of reduced states as a complementary probe of quantum criticality and provide further insight into the role of non-stabilizer resources in many-body quantum phase transitions.