SO(3)lver

SO(3)lver is an extension of the package FuzzifiED. It 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 package, include at the start of the Julia script

using FuzzifiED
using FuzzifiED.SO3lver

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

Implementing Full $\mathrm{SO}(3)$ Rotation Symmetry for Exact Diagonalization on the Fuzzy Sphere, Zheng Zhou and Yin-Chen He, arXiv:2509.xxxxx (to appear).

SO(3)lver

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