[論文レビュー] Two-Point Stabilizer Rényi Entropy: a Computable Magic Proxy of Interacting Fermions

Jun Qi Fang, Fo-Hong Wang+1 more|arXiv (Cornell University)|Jan 19, 2026

Quantum many-body systems被引用数 0

ひとこと要約

要約: The paper introduces the two-point stabilizer Rényi entropy (SRE) and its mutual form as computable probes of magic in interacting fermions, usable with DQMC and DMRG to detect phase transitions and topological textures.

ABSTRACT

Quantifying non-stabilizerness (``magic'') in interacting fermionic systems remains a formidable challenge, particularly for extracting high order correlations from quantum Monte Carlo simulations. In this Letter, we establish the two-point stabilizer Rényi entropy (SRE) and its mutual counterpart as robust, computationally accessible probes for detecting magic in diverse fermionic phases. By deriving local estimators suitable for advanced numerical methods, we demonstrate that these metrics effectively characterize quantum phase transitions: in the one-dimensional spinless $t$-$V$ model, they sharply identify the Luttinger liquid to charge density wave transition, while in the two-dimensional honeycomb lattice via determinant quantum Monte Carlo, they faithfully capture the critical exponents of the Gross-Neveu-Ising universality class. Furthermore, extending our analysis to the fractional quantum Hall regime, we unveil a non-trivial spatial texture of magic in the Laughlin state, revealing signatures of short-range exclusion correlations. Our results validate the two-point SRE as a versatile and sensitive diagnostic, forging a novel link between quantum resource theory, critical phenomena, and topological order in strongly correlated matter.

研究の動機と目的

• Define and motivate the two-point stabilizer Rényi entropy (SRE) as a practical magic measure for fermions.
• Develop local estimators suitable for determinant quantum Monte Carlo (DQMC) to evaluate two-point SRE.
• Demonstrate that two-point SRE detects quantum phase transitions in 1D and 2D fermionic models.
• Explore magic textures in fractional quantum Hall states and relate SRE to topological and critical phenomena.

提案手法

• Define rank-α stabilizer Rényi entropy M_α(ρ) and its two-point version M_i,j^(α)(ρ) for reduced density matrices.
• Map the Pauli string sum to Majorana monomials to compute SRE efficiently for fermionic Gaussian states.
• Implement a two-level Monte Carlo scheme (sampling auxiliary fields and Majorana strings) within the DQMC framework.
• Use mutual two-point SRE: ̃M_i,j^(α)(ρ) = M_i,j^(α)(ρ) − M_i^(α)(ρ) − M_j^(α)(ρ) to isolate correlation-induced magic.
• Apply the framework to the 1D half-filled t−V model and the 2D honeycomb lattice to extract critical behavior.
• Analyze the Laughlin ν=1/3 state to reveal spatial textures of magic and their relation to orbital structure.

実験結果

リサーチクエスチョン

• RQ1 Can two-point stabilizer Rényi entropy serve as a reliable, computable witness of non-stabilizerness (magic) in interacting fermions?
• RQ2 Do two-point SRE and its mutual form act as sharp detectors of fermionic quantum phase transitions in 1D and 2D systems?
• RQ3 What are the critical exponents and universality classes revealed by SRE-based scaling analyses in fermionic models?
• RQ4 How does magic manifest spatially in topologically ordered states such as the Laughlin fractional quantum Hall state?

主な発見

• Two-point SRE functions as an effective local proxy for global magic, identifying local non-Clifford resources.
• In 1D, the mutual two-point SRE signals the LL to CDW transition and captures finite-size BKT scaling via V_c(L).
• In 2D honeycomb systems, the mutual two-point SRE reveals the Gross-Neveu-Ising universality class through finite-size scaling.
• In the Laughlin ν=1/3 state, magic shows a plateau at short range due to exclusion of low relative angular momentum channels, revealing orbital texture.
• The mutual two-point SRE provides a robust diagnostic linking quantum magic with fermionic criticality and topological order.