Never heard of high power lights causing their colors to fade. What will cause their colors to fade is if they are kept alone without other anthias of the same species to display to one another.
On another note i would not recomend square back anthias for a 120 gallon tank as they do get fairly large and would need a little more room since they do best in a small group, a better choice would be lyretails, bartletts, Hutchi, bicolors among others.