Tripartite information of free fermions: a universal entanglement coefficient from the sine kernel

• URL: http://arxiv.org/abs/2603.03103v2
• Date: Wed, 04 Mar 2026 19:27:31 GMT
• Title: Tripartite information of free fermions: a universal entanglement coefficient from the sine kernel
• Authors: Aleksandrs Sokolovs,
• Abstract summary: We study the tripartite information I_3 of free fermions on two-dimensional lattices partitioned into three adjacent strips of width w.<n>We prove that g(z) has a unique zero at z* = 1.3288: modes with k_F w z* violate monogamy of mutual information (g > 0)<n>We verify all predictions on square, triangular, and cubic lattices.
• Score: 51.56484100374058
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the tripartite information I_3 of free fermions on two-dimensional lattices partitioned into three adjacent strips of width w. Translation invariance yields the exact decomposition I_3 = sum_{k_y} g(k_F(k_y) w), where g(z) is a universal function of the scaling variable z = k_F w, determined by the spectrum of the sine-kernel (Slepian) integral operator. We prove that g(z) has a unique zero at z* = 1.3288: modes with k_F w < z* violate monogamy of mutual information (g > 0), while modes with k_F w > z* satisfy it (g < 0). The central analytical result is g(z) = cz + O(z^3 ln z) with c = 3 ln(4/3)/pi, derived from the rank-1 limit of the sine kernel. Two exact cancellations -- of the z ln z area-law terms and of the z^2 terms -- are intrinsic to the I_3 combination. The coefficient c generalizes to n-partite information: c_n = (n/pi) ln R_n with R_n a rational number from binomial combinatorics. For Renyi entropy of index alpha, we prove that g_alpha(z) ~ z^alpha for alpha < 2 and g_2(z) = -(8/pi^3) z^3: von Neumann entropy (alpha = 1) uniquely gives linear sensitivity to Lifshitz transitions, while Renyi-2 gives only cubic sensitivity. We verify all predictions on square, triangular, and cubic lattices.

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