Quantum phase transitions and geometric phases

Quantum phase transition is one of main interests in the field of condensed matter physics. Similarly, geometric phases arrest considerable interest in the field of quantum mechanics. However, no any relevant relation was recognized before recent work. In this communication, we mainly introduce the recent results on the connections between quantum phase transitions and geometric phases: a non-contractible geometric phase is a signature of quantum phase transitions, especially all key ingredients of quantum criticality are present in geometric phases of the ground state. These results may arrest interest from both communities.