Stabilizer-Rényi Microscopy of Critical Correlations in Interacting Fermions

[2601.13314] Stabilizer-Rényi Microscopy of Critical Correlations in Interacting Fermions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Strongly Correlated Electrons arXiv:2601.13314 (cond-mat) [Submitted on 19 Jan 2026 ( v1 ), last revised 15 Aug 2026 (this version, v3)] Title: Stabilizer-Rényi Microscopy of Critical Correlations in Interacting Fermions Authors: Jun Qi Fang , Fo-Hong Wang , Xiao Yan Xu View a PDF of the paper titled Stabilizer-R\'enyi Microscopy of Critical Correlations in Interacting Fermions, by Jun Qi Fang and 1 other authors View PDF HTML (experimental) Abstract: Quantum magic---the resource that separates universal quantum computation from efficiently simulable Clifford circuits---has emerged as a diagnostic of many-body quantum states, yet the stabilizer Rényi entropy (SRE) that quantifies it remains largely inaccessible in interacting fermion systems. Estimating the global SRE requires a sum over exponentially many Majorana strings, which in determinant quantum Monte Carlo can be sampled without a sign problem only for the interacting density matrix obtained after averaging the auxiliary fields: sampling strings and fields simultaneously incurs a sign problem even for sign-problem-free models, so that the known sign-free alternative is a nested Monte Carlo that does not scale. We propose instead the two-point SRE---a practical stabilizer-Rényi correlator built from rank-2 SREs of one- and two-site reduced density matrices, which are fixed exactly by single-particle Green functions and density correlations already measured in standard simulations---and show that it obeys universal finite-size scaling at fermionic quantum critical points. In the one-dimensional half-filled spinless $t$-$V$ chain, the correlator distinguishes algebraic and exponential decay regimes and tracks the inverse-logarithmic finite-size drift characteristic of the Berezinskii--Kosterlitz--Thouless transition. On the honeycomb lattice, sign-problem-free quantum Monte Carlo yields Gross--Neveu--Ising scaling with finite anomalous dimension at zero temperature and two-dimensional Ising collapse at the thermal transition. Our results suggest stabilizer-Rényi microscopy as a spatially resolved, quantitatively universal probe of critical correlations in interacting fermionic matter, on par with conventional order-parameter correlators and accessible to quantum-simulator measurements. Subjects: Strongly Correlated Electrons (cond-mat.str-el) ; High Energy Physics - Lattice (hep-lat); Quantum Physics (quant-ph) Cite as: arXiv:2601.13314 [cond-mat.str-el] (or arXiv:2601.13314v3 [cond-mat.str-el] for this version) https://doi.org/10.48550/arXiv.2601.13314 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jun Qi Fang [ view email ] [v1] Mon, 19 Jan 2026 19:00:03 UTC (1,200 KB) [v2] Wed, 28 Jan 2026 07:54:05 UTC (1,200 KB) [v3] Sat, 15 Aug 2026 13:31:09 UTC (1,381 KB) Full-text links: Access Paper: View a PDF of the paper titled Stabilizer-R\'enyi Microscopy of Critical Correlations in Interacting Fermions, by Jun Qi Fang and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.str-el < prev | next > new | recent | 2026-01 Change to browse by: cond-mat hep-lat quant-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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