Here is the passage again:
Phillip left work early. To memorize the vocabulary that his Spanish midterm would test the next day. But all that he could think about was Beatrice, the cute new sales associate who worked in the camera department.
To memorize, an infinitive, begins this fragment, so you can call it an infinitive phrase fragment. Between the first word, to, and the last word, day, there is no main clause. Every sentence must contain at least one main clause.