Rényi exponent landscape of multipartite entanglement in free-fermion systems

• URL: http://arxiv.org/abs/2603.08991v1
• Date: Mon, 09 Mar 2026 22:27:00 GMT
• Title: Rényi exponent landscape of multipartite entanglement in free-fermion systems
• Abstract summary: We show that the Rényi tripartite information $I_3() exhibits a qualitatively $exclusion-dependent scaling at small Fermi momentum.<n>A direct consequence is a replica obstruction: $I_m(n)/I_m(1) sim zm-1 to 0$ for all integer $n geq 2$, so the leading von Neumann signal cannot be reconstructed from integer Rényi data.
• Score: 51.56484100374058
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that the Rényi tripartite information $I_3^{(α)}$ of free fermions exhibits a qualitatively $α$-dependent scaling at small Fermi momentum, in sharp contrast to bipartite entropy where only the prefactor changes. In the rank-1 regime ($z = k_F w \ll 1$), $I_3^{(α)}$ receives contributions from two competing channels -- a fractional-moment channel $\sim z^α$ (active for non-integer $α$) and a polynomial channel $\sim z^m$ from the first nonvanishing inclusion-exclusion moment $σ_m$ -- yielding the scaling exponent $β_m(α) = \min(α, m)$ for $m$-partite information of $m$ adjacent strips. Integer Rényi indices $α= 2, 3, \ldots$ are anomalous: the fractional channel closes and the exponent jumps to $m$ or higher. A direct consequence is a replica obstruction: $I_m^{(n)}/I_m^{(1)} \sim z^{m-1} \to 0$ for all integer $n \geq 2$, so the leading von Neumann signal cannot be reconstructed from integer Rényi data at the level of leading scaling -- a situation with no bipartite analog. Conversely, negativity-based measures ($α= 1/2$) give a $20\times$ enhanced signal compared to von Neumann. We derive the underlying product formula for the coefficient $c(w_A, w_B, w_D)$, prove an $m$-partite generating function for the inclusion-exclusion moments, and verify all results numerically to high precision.

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