The fidelity approach to quantum phase transitions

The fidelity approach to critical phenomena is based on differential geometry and information theory. ground states corresponding to Hamiltonians with infinitesimally close parameters sets are analyzed by using their ground state quantum fidelity a.. the modulus of th overlap of the corresponding ground states The fidelity analysis is not based on the a priori identification of an order parameter, and hence does not require knowledge of symmetry breaking patterns or more generally the analysis of any distinguished observable Instead, it is purely metric and can thus be formulated in terms of the singularities of a universal metric tensor on the Hamiltonian parameter space In this paper we provide an overview of our main contributions in this field