Spectral optimization of spherical lattices and applications to classical and quantum interacting spin systems

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 (2ℓ+1), ℓ=0,1,2,…, continuum multiplets expected from 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.

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BibTeX RIS

BibTeX

@misc{voller2026spectral,
  title = {{Spectral optimization of spherical lattices and applications to classical and quantum interacting spin systems}},
  author = {Jonas Völler and Grigorios Makris and Fabian Hassler and Stefan Wessel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12663},
  eprint = {2610.12663},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12663},
}

RIS

TY  - UNPB
TI  - Spectral optimization of spherical lattices and applications to classical and quantum interacting spin systems
AU  - Jonas Völler
AU  - Grigorios Makris
AU  - Fabian Hassler
AU  - Stefan Wessel
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12663
UR  - https://arxiv.org/abs/2610.12663
AB  - 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 (2ℓ+1), ℓ=0,1,2,…, continuum multiplets expected from 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.
ER  -

Abstract

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