H is the Hamiltonian. Here we set µ=0. For grand-canonical calculations add -6µ to the main diagonal.

2*h	0	0	-2*Sqrt[2]*t
0	2*h + U	-2*Sqrt[2]*t	0
0	-2*Sqrt[2]*t	2*h + U	-2*t
-2*Sqrt[2]*t	0	-2*t	2*h + U