Generators of stability-preserving semigroups, spectral gaps, and classical ground-state computation

arXiv:2609.26802 · math.CV, math-ph, math.CO, math.MP, quant-ph · Submitted 2026-09-13 · Read on arXiv

math.CV, math-ph, math.CO, math.MP, quant-ph

Submitted: 2026-09-13

Updated: 2026-09-24

Comments: 64 pages. Substantially reorganized and rewritten for clarity; references updated, including independent work by Jiang (arXiv:2609.25037). Mathematical results unchanged; theorem numbering changed. Exact verification scripts included as ancillary files

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Spectral Gap — 41× in this paper · explained in 5 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Trace — 3× in this paper · explained in 2 episodes
• Verification — 3× in this paper · explained in 2 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Homogeneity — 2× in this paper · explained in 2 episodes
• Adaptive Strategy — 1× in this paper · explained in 1 episode
• Adjacency Matrix — 1× in this paper · explained in 1 episode
• Admissibility — 1× in this paper · explained in 2 episodes
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes

Sources

• Conjectured Bounds for 2-Local Hamiltonians via Token Graphs
• Sharp Bounds on the Eigenvalues of Kikuchi Graphs and Applications to Quantum Max Cut
• Efficient quantum algorithm for Heisenberg spin systems
• Discrete Concavity of Token-Graph Spectral Radii via Lorentzian Semigroups
• A complexity phase transition at the EPR Hamiltonian
• Fast mixing of operator-loop path-integral quantum Monte Carlo for stoquastic XY Hamiltonians
• Spectral gap of Lee-Yang Hamiltonians
• Rapidly mixing loop representation quantum Monte Carlo for Heisenberg models on star-like bipartite graphs
• Lie-algebraic approach to the theory of polynomial solutions. I. Ordinary differential equations and finite-difference equations in one variable
• Lie-algebras and linear operators with invariant subspaces
• Lee-Yang tensors and Hamiltonian complexity