SO(3)lver

The module SO(3)lver enables exact diagonalization (ED) on the fuzzy sphere with the implementation of full $\mathrm{SO}(3)$ spatial rotation symmetry and some non-Abelian flavour symmetry through partitioning the Hilbert space into segments and compose these segments.

The implementation of $\mathrm{SO}(3)$ symmetry greatly reduces the demand for the memory and enables calculation for much larger size. E. g., with the $\mathrm{SO}(3)$ resolution, the Hilbert space of the ground-state sector for $N_m=22$ has a dimension $2.07\times 10^7$, and the Hamiltonian requires a memory of 76.5 Go ; as a comparison, without the $\mathrm{SO}(3)$ resolution, the Hilbert space for $N_m=18$ has a similar dimension $2.84\times 10^7$, and the Hamiltonian requires a memory of 63.9 Go.

SO(3)lver can apply to a lot of current fuzzy-sphere research. Its flexible design also makes it straightforward to adapt to new models. We provide a collection of examples.

To use the module, include also at the start of your Julia script

using FuzzifiED.SO3lver

If this module is helpful in your research, please cite :

Advancing Fuzzy-Sphere CFTs : $\mathrm{SO}(3)$-Rotation-Resolving Exact Diagonalization, 3D Ising Heavy Primaries, and Quasi-Hole-Space Projection, Zheng Zhou and Yin-Chen He arXiv:2609.35960

SO(3)lver

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