Spectral optimization of spherical lattices and applications to classical and quantum interacting spin systems
Year: 2026
Type: preprint
Abstract: We develop an optimization algorithm for spherical lattice discretizations based on the spectrum of the discretized Laplace operator. Starting from refined icosahedral lattices, we minimize the splitting of the $(2\ell+1)$, $\ell=0,1,2,\dots$, continuum multiplets expected from $\mathrm{SO}(3)$ symmetry via gradient descent. This approach simultaneously produces lattices based on triangles with nearly uniform circumradii and perimeters. Although the optimization uses only the free-particle spectrum, we show that the resulting lattices carry over to interacting models. On the optimized lattices, rotational symmetry is restored for the critical Ising and Potts models and primary scaling dimensions are accurately reproduced for the three-dimensional Ising conformal field theory, when appropriate geometry-dependent interaction strengths are used. Higher-angular-momentum descendant states reveal weak residual symmetry breaking beyond the sectors protected by the underlying icosahedral symmetry.
Source: arXiv (Cornell University)
Institution: RWTH Aachen University
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: RWTH Aachen University
OpenAlex ID: W7221543397