  Quantum phase transition is one of the main interests in the field of
condensed matter physics, while geometric phase is a fundamental concept and
has attracted considerable interest in the field of quantum mechanics. However,
no relevant relation was recognized before recent work. In this paper, we
present a review of the connection recently established between these two
interesting fields: investigations in the geometric phase of the many-body
systems have revealed so-called "criticality of geometric phase", in which
geometric phase associated with the many-body ground state exhibits
universality, or scaling behavior in the vicinity of the critical point. In
addition, we address the recent advances on the connection of some other
geometric quantities and quantum phase transitions. The closed relation
recently recognized between quantum phase transitions and some of geometric
quantities may open attractive avenues and fruitful dialog between different
scientific communities.
