T-J model on Penrose lattice

In recent years, quasicrystals have attracted extensive research. They lack translational symmetry, but have rotational symmetry that does not exist in crystals. Penrose lattice is a typical two-dimensional quasicrystalline structure. We studied the t-j model on the penrose lattice. First, we use the mean-field method to process the Hamiltonian in real space, and then self-consistently solve the BdG equation. In the end, we got the result that the ground state of the s wave generally has the lowest energy under different doping conditions, and these ground states satisfy Anderson's theorem.