I thoroughly enjoy getting lost in the writing of Donna Tartt, particularly The Secret History.
I think a comma is correct. A semicolon would separate two main clauses, but the second part of the sentence is not a main clause (it is not a sentence by itself and has no verb). The comma is used because the second part adds more information on to the sentence.
you do not need a semicolon. remember semicolons cannot be used before a dependent clause only a dependent. Ask yourself if this clause can stand alone as a sentence; this means an independent clause must be a complete thought with a verb and noun.
Semi-colons are only used to join Two independent clauses. particularly The Secret History cannot 'stand by itself' if that makes sense.