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

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