Parity superselection obstructs monogamy of mutual information in free fermions
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914408093974528 |
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| author | Sokolovs, Aleksandrs |
| author_facet | Sokolovs, Aleksandrs |
| contents | We prove that free fermions in the spin (tensor product) factorization violate monogamy of mutual information: $I_3^{\mathrm{spin}} > 0$ for adjacent strips of width $w \le 6$ at all Fermi momenta, and for all $w$ at $z = k_F w < z^* \approx 1.329$. Many-body computation at $w=6$ via the $G$-matrix formula maps the scaling-limit function $I_3^{\mathrm{spin}}(z)$: it has a minimum of $0.100$ at $z \approx 1.5$, numerically establishing the conjecture $I_3^{\mathrm{spin}} > 0$ for all $z$ and $w$.
The proof rests on an exact identity: the fermionic and spin reduced density matrices of disjoint regions $A$, $D$ separated by $B$ differ by the parity insertion $(-1)^{N_B}$ in the partial trace. A Perron--Frobenius argument proves element-wise coherence damping; for free fermions, an independent Gaussian bound gives the entropy ordering $ΔS_{AD} \ge 0$. Exact diagonalization confirms this for interacting fermions.
DMRG on the $t$-$V$ chain shows that the factorization contribution exceeds the genuine interaction contribution to $I_3$ by a factor of 8, accounting for $\sim 80\%$ of the deviation in spin-basis numerics. Strong repulsion ($K \lesssim 0.7$) restores monogamy. Conversely, $Z_2$ parity superselection enforces $I_3 \le 0$ at all fillings (proved for $w \le 3$), with the ratio of parity entropy to quantum excess approaching $2\ln 2/(3\ln(4/3)) = 1.606$.
Any use of $I_3$ as a diagnostic for holographic duality, quantum chaos, or Fermi surface topology must specify the operator algebra; without this, the sign of $I_3$ is ambiguous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14154 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parity superselection obstructs monogamy of mutual information in free fermions Sokolovs, Aleksandrs Statistical Mechanics We prove that free fermions in the spin (tensor product) factorization violate monogamy of mutual information: $I_3^{\mathrm{spin}} > 0$ for adjacent strips of width $w \le 6$ at all Fermi momenta, and for all $w$ at $z = k_F w < z^* \approx 1.329$. Many-body computation at $w=6$ via the $G$-matrix formula maps the scaling-limit function $I_3^{\mathrm{spin}}(z)$: it has a minimum of $0.100$ at $z \approx 1.5$, numerically establishing the conjecture $I_3^{\mathrm{spin}} > 0$ for all $z$ and $w$. The proof rests on an exact identity: the fermionic and spin reduced density matrices of disjoint regions $A$, $D$ separated by $B$ differ by the parity insertion $(-1)^{N_B}$ in the partial trace. A Perron--Frobenius argument proves element-wise coherence damping; for free fermions, an independent Gaussian bound gives the entropy ordering $ΔS_{AD} \ge 0$. Exact diagonalization confirms this for interacting fermions. DMRG on the $t$-$V$ chain shows that the factorization contribution exceeds the genuine interaction contribution to $I_3$ by a factor of 8, accounting for $\sim 80\%$ of the deviation in spin-basis numerics. Strong repulsion ($K \lesssim 0.7$) restores monogamy. Conversely, $Z_2$ parity superselection enforces $I_3 \le 0$ at all fillings (proved for $w \le 3$), with the ratio of parity entropy to quantum excess approaching $2\ln 2/(3\ln(4/3)) = 1.606$. Any use of $I_3$ as a diagnostic for holographic duality, quantum chaos, or Fermi surface topology must specify the operator algebra; without this, the sign of $I_3$ is ambiguous. |
| title | Parity superselection obstructs monogamy of mutual information in free fermions |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2603.14154 |