Quantum phase transition and quantum fidelity

Finite size scaling is an important tool to study the "critical behavior" of a finite system. On the other hand, quantum fidelity is a quantum information theoretic measure that can efficiently detect a quantum critical point for a finite quantum system. In this talk, I shall show that the scaling of fidelity in different limits can be derived in a straightforward fashion simply using the notion of the finite size scaling analyzing different length scales involved in the problem. I shall also indicate situations (known as the "marginal situation") where the fidelity approach fails to detect a quantum critical point.