QGN stiffness conjecture
QGN stiffness conjecture
For every quantum geometric nesting (QGN) model with an exact frustration-free ground state and a spontaneously broken continuous symmetry, the exact stiffness associated with that symmetry equals the stiffness obtained by restricting the calculation to the Gaussian variational manifold: .
References
Primary source
Additional references
Progress summary
A recent unrefereed preprint claims to prove the conjecture for a special class of solvable quantum systems, but independent confirmation is absent.
The conjecture concerns exact formulas for stiffness and response functions in solvable QGN models. The reported result claims a complete resolution within that model class, not beyond it.
Known results
- Foundational QGN work constructs solvable interacting flat-band systems and computes phase stiffness exactly in ideal cases (2024).
- Numerical and bootstrap studies find close agreement with the conjectured stiffness formula, including exact agreement on a small system, but explicitly leave a rigorous proof open.
August 27, 2026 claimed proof
A linked preprint is reported to use Fock-space fragmentation to show that an infinitesimal phase twist couples the ground state only to the one-particle, one-hole sector, yielding exact stiffness and response functions for QGN models. This is a claimed solution and remains unverified; independently retrieved arXiv material instead describes bootstrap evidence and says a rigorous proof remains future work.
Current status (as of August 2026): A preprint claims a complete proof for QGN models, but the conjecture remains unverified and its scope beyond QGN models is unresolved.
Sources
- arxiv.org
- browse.arxiv.org
- arxiv.org
- arxiv.org
- pmc.ncbi.nlm.nih.gov
- ntrs.nasa.gov
- dspace.mit.edu
- quantamagazine.org
- quantamagazine.org
- quantamagazine.org
- scientificamerican.com
- arxiv.org
- arxiv.org
- arxiv.org
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- community.openai.com
- quantamagazine.org
- quantamagazine.org
Solutions 0
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