Tripartite information of free fermions: a universal entanglement coefficient from the sine kernel
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908871363133440 |
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| author | Sokolovs, Aleksandrs |
| author_facet | Sokolovs, Aleksandrs |
| contents | 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 find that g(z) has a unique zero at z* = 1.329 +/- 0.001: 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 ~ 0.2747, 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 show 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. DMRG calculations on the interacting t-V model provide evidence that the linear coefficient is independent of the Luttinger parameter K. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tripartite information of free fermions: a universal entanglement coefficient from the sine kernel Sokolovs, Aleksandrs Statistical Mechanics Quantum Physics 81P40, 82B10 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 find that g(z) has a unique zero at z* = 1.329 +/- 0.001: 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 ~ 0.2747, 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 show 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. DMRG calculations on the interacting t-V model provide evidence that the linear coefficient is independent of the Luttinger parameter K. |
| title | Tripartite information of free fermions: a universal entanglement coefficient from the sine kernel |
| topic | Statistical Mechanics Quantum Physics 81P40, 82B10 |
| url | https://arxiv.org/abs/2603.03103 |