Explicit Volume-Uniform Gap Bounds for Weakly Coupled SU(3) Cube Blocks on Three-Dimensional Lattices - Charged responses, signed output Gram matrices, and local preconditioning-
Year: 2026
Type: preprint
Abstract: We give explicit sufficient conditions for a spectral gap uniform in the number of sites of a three-dimensional SU(3) Hamiltonian lattice, partitioned into disjoint cube blocks and free bridge links. Using previously certified one-cube spectral and comparison bounds, we obtain a dimensionless gap at least 2/9, on the full kinematic Hilbert space and hence on its Gauss-invariant subspace, for inter-block plaquette strength 0 ≤ s ≤ 1/6144. The point s = 1 is the isotropic Kogut–Susskind lattice at β = 1/2 in our Hamiltonian convention. The argument combines a gauge-Casimir comparison, a product-vacuum fixed-point construction, an excitation resolvent criterion, and orthogonal-output estimates with constants independent of volume. An isolated two-cube, two-bridge block has a full kinematic gap at least 1/3 at s = 1. For a four-face interface we retain all signed entries of an 18-vector output Gram matrix, reducing a specified residual upper bound from 0.160048 to 0.146438. Explicit bounded shears improve the derivative on the one-edge charged input subspace and eliminate its columns in an origin-level excitation test. These shears act trivially on the physical neutral sector; neither they nor the interface Gram establish a full-input contraction at s = 1. The particular derivative majorant used for the global theorem cannot certify s ≥ 1/4860; this is not a no-go result for other methods. The scope of the inherited certificates and the remaining thermodynamic and continuum questions are stated separately.
Author: Umeno, Ken
Institution: Kyoto University
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225017903