What question did this study set out to answer?

The aim is to establish a connection between acyclicity in directed graphs and spectral gaps in frustration-free spin chains.

August 6, 2026Open Access

A fixed-level certification dichotomy for an infinite family of frustration-free spin chains

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The aim is to establish a connection between acyclicity in directed graphs and spectral gaps in frustration-free spin chains.
Attached a rational frustration-free spin-chain interaction to every finite loopless directed graph.
Developed a certification hierarchy and established exact relationships between graph properties and spectral gaps.
Used both analytical and computational methods, including exact symbolic arithmetic to derive results.
Established that acyclicity implies a non-zero spectral gap (liminf_m gap_m(T) > 0) with precise bounds.
Provided a quantitative assessment of cyclic cases using free-fermion analysis with computed energy modes.
Demonstrated a fixed-level completeness result for the spectral-gap certification hierarchy over an infinite chain family.

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Implication

Randomized trial shows fixed-level certification linked to spectral gap in infinite frustration-free spin chains, suggesting a unique combinatorial approach.

Cite This Study

Guillaume Lecomte (2026) studied this question.

synapsesocial.com/papers/6a74379d764cddc9499d4fc0 https://doi.org/10.5281/zenodo.21790823

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Implication

Randomized trial shows fixed-level certification linked to spectral gap in infinite frustration-free spin chains, suggesting a unique combinatorial approach.

A fixed-level certification dichotomy for an infinite family of frustration-free spin chains

Key Points

Discussion

Implication

Cite This Study

A fixed-level certification dichotomy for an infinite family of frustration-free spin chains

Key Points

Discussion

Implication

Cite This Study

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