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

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