arXiv subjects

Aleksandrs Sokolovs

Publications and source records attributed to Aleksandrs Sokolovs.

3 recordsLinked to original sources

arXiv2026

Parity superselection obstructs monogamy of mutual information in free fermions

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.

cond-mat.stat-mech↗

arXiv2026

Rényi exponent landscape of multipartite entanglement in free-fermion systems

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.

cond-mat.stat-mech↗

arXiv2026

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

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.

cond-mat.stat-mech↗