bibkey: fukaiyoshidakatsura2026dissipative authors: K. Fukai; H. Yoshida; H. Katsura year: 2026 title: “Dissipative free fermions in disguise” doi: 10.48550/arXiv.2603.22163 url: https://arxiv.org/abs/2603.22163v1 claim: “The expectation after Eq. (17) places every root of the plus dissipative independence polynomial in the open upper half-plane for ECF graphs, under the standing shared-root exclusion after Eq. (26).” strata_touched:

• D5/S3/Quantum/SpinChains/DissipativeFreeFermionRootLocation license: citation-only triage: anchor

Fukai, Yoshida and Katsura, dissipative free fermions in disguise

Printed p. 4, after Eq. (17):

We expect Im ũ_k > 0 to hold for general ECF graphs, as observed numerically in the boundary-driven Fendley model, so that ε̃_k ≡ 1/ũ_k satisfies Im ε̃_k < 0.

The roots ũ_k are those of the plus polynomial in Eq. (16), printed p. 4:

$${\tilde{P}}_G^{\pm }(u)\equiv P_G(u^2)\pm i\gamma u{P}_{G\setminus K_s}(u^2).$$

Printed p. 3, Eq. (7):

The independence polynomial is defined as

$$P_G(x)\equiv \sum _{S\in {\mathcal{S}}_G}(-x{)}^{|S|}\prod _{j\in S}{b}_j^2,$$

where S_G denotes the collection of all independent sets.

Printed p. 2:

A graph is claw-free if it has no claw as an induced subgraph (Fig. 1(a)), and even-hole-free if it has no even hole as an induced subgraph (Fig. 1(b)).

The couplings b_j are real and γ > 0 is the dissipation rate in the jump operator ℓ = √γ χ. ECF means even-hole-free and claw-free. Printed p. 3:

The edge operator χ is associated with a clique K_s ⊆ V(G), i.e., a subset of mutually adjacent vertices.

Equivalently, denoting the closed neighborhood of j by Γ[j] ≡ {j} ∪ {ℓ ∈ V(G) | A_jℓ = 1}, K_s is simplicial if and only if Γ[j] \ K_s is a clique for all j ∈ K_s.

Printed p. 7, after Eq. (26):

Equation (26) shows that N_k = 0 if P_G and P_{G\K_s} share the root u_k². Throughout this work, we exclude this nongeneric case [80].

The root statement retains this exclusion. Its proof uses finite-clique deletion and a positive-imaginary multiplier for points in the lower half-plane. Even-hole-freeness is retained in the source statement but is unused by the proof. The Liouvillian spectral interpretation and gap formula are the paper’s derivation; they are not separate Lean statements here. Common-root cases and quantitative uniform root-height bounds remain separate questions.

Verified locator

• DOI: https://doi.org/10.48550/arXiv.2603.22163
• URL: https://arxiv.org/abs/2603.22163v1
• Version 1, printed pp. 3–4 (Eqs. (7), (16), simpliciality and the expectation), printed p. 7 (Eq. (26) and the standing exclusion).