Stabilizer-R\'enyi Microscopy of Critical Correlations in Interacting Fermions

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.

Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Lattice (hep-lat); Quantum Physics (quant-ph)

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

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