Archaic, perhaps, in the sense that it's loyal to original Mother Tongue, but not archaic if you mean learnt is no longer an appropriate past tense or past participle of the verb learn.
The Oxford English Dictionary - the OED - doesn't say learnt is archaic, it says it's 'chiefly British.'
Again, that's the OED, the definitive dictionary of the English language, all 20 volumes and and 21,728 pages of it.
well ok, I just think it is irritating, learnt burnt etc but I understand