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

2*U	Sqrt[3]*t	0	0	0	0	0	0	0	Sqrt[3]*t	0	0
Sqrt[3]*t	2*U	-(Sqrt[6]*t)	0	0	0	0	-t	Sqrt[2]*t	0	t	-(Sqrt[2]*t)
0	-(Sqrt[6]*t)	2*U	0	0	0	0	0	0	0	0	0
0	0	0	0	0	((3*Sqrt[2] + Sqrt[3])*t)/Sqrt[6 + Sqrt[6]]	-(((Sqrt[2] - 3*Sqrt[3])*t)/Sqrt[6 + Sqrt[6]])	0	0	0	0	0
0	0	0	0	0	(3*(-1 + Sqrt[6])*t)/Sqrt[18 - 3*Sqrt[6]]	-((Sqrt[2/(6 - Sqrt[6])] + 3*Sqrt[3/(6 - Sqrt[6])])*t)	0	0	0	0	0
0	0	0	((3*Sqrt[2] + Sqrt[3])*t)/Sqrt[6 + Sqrt[6]]	(3*(-1 + Sqrt[6])*t)/Sqrt[18 - 3*Sqrt[6]]	U	0	-(Sqrt[2]*t)	0	0	0	-2*t
0	0	0	-(((Sqrt[2] - 3*Sqrt[3])*t)/Sqrt[6 + Sqrt[6]])	-((Sqrt[2/(6 - Sqrt[6])] + 3*Sqrt[3/(6 - Sqrt[6])])*t)	0	U	0	-2*t	0	-2*Sqrt[2]*t	2*t
0	-t	0	0	0	-(Sqrt[2]*t)	0	U	0	-2*t	0	0
0	Sqrt[2]*t	0	0	0	0	-2*t	0	U	0	0	0
Sqrt[3]*t	0	0	0	0	0	0	-2*t	0	U	-t	0
0	t	0	0	0	0	-2*Sqrt[2]*t	0	0	-t	2*U	0
0	-(Sqrt[2]*t)	0	0	0	-2*t	2*t	0	0	0	0	2*U