bibkey: sokolovs2026paritysuperselection
authors: Aleksandrs Sokolovs
year: 2026
title: "Parity superselection obstructs monogamy of mutual information in free fermions"
doi: null
url: https://arxiv.org/abs/2603.14154v2
claim: "For ground states of fermionic Hamiltonians with real non-positive hopping, the parity-twisted partial trace satisfies |rho^tw_ij| <= rho^spin_ij = |rho^spin_ij| on D-parity-changing elements (Theorem 1); whether this coherence damping extends to complex hopping or frustrated lattices is stated as open."
strata_touched:
  - D5/S3/Quantum/SpinChains/ComplexHoppingCoherenceDampingRefutation
license: citation-only
triage: anchor

Parity superselection obstructs monogamy of mutual information in free fermions

Aleksandrs Sokolovs, arXiv:2603.14154v2 (cond-mat.stat-mech), 2026-03-18. Quotations are from the v2 TeX source.

The two partial traces (Section 3):

\textbf{Spin trace.} ${\rho }_{n_A{n}_D,n_A^{\prime }{n}_D^{\prime }}^{\mathrm{spin}}={\sum }_{n_B}⟨n_A{n}_B{n}_D|{\rho }_{ABD}|n_A^{\prime }{n}_B{n}_D^{\prime }⟩$. Define the parity-twisted partial trace ${\rho }_{AD}^{\mathrm{tw}}={\mathrm{tr}}_B[(-1{)}^{N_B}{\rho }_{ABD}]$.

Coherence damping (Theorem 1):

Let $H$ be a fermionic Hamiltonian with real non-positive hopping ($H_{\alpha \beta }\le 0$ for $\alpha \ne \beta$ in the occupation basis). For the ground state and any tripartition into adjacent blocks $A$, $B$, $D$: |\rho_{ij}^{\mathrm{tw}}| \le \rho_{ij}^{\mathrm{spin}} = |\rho_{ij}^{\mathrm{spin}}| for all $D$-parity-changing matrix elements of ${\rho }_{AD}={\mathrm{Tr}}_{BE}|\psi ⟩⟨\psi |$.

The open problem (Section 7):

Theorem~\ref{thm:damping} settles the coherence damping inequality for ground states with real non-positive hopping; whether it extends to systems with complex hopping (e.g., in a magnetic field) or frustrated lattices remains open.

Verified locator

• URL: https://arxiv.org/abs/2603.14154v2 (v2, 2026-03-18; source paper3.tex, md5 218ffddeea8a18ac5e6261c39231afc9): the partial traces (l. 112–121), Theorem 1 (l. 143–150) and the open problem (l. 355).