Renormalization group flows and quantum phase transitions: fidelity versus entanglement

Understand

We compare the roles of fidelity and entanglement in characterizing renormalization group flows and quantum phase transitions.

• It turns out that the scaling parameter extracted from fidelity for different ground states succeeds to capture nontrivial information including stable and unstable fixed points, whereas the von Neumann entropy as a bipartite entanglement measure (or equivalently, majorization relations satisfied by the spectra of the reduced density matrix along renormalization group flows) often fails, as far as the intrinsic irreversibility-information loss along renormalization group flows-is concerned.
• We also clarify an intimate connection between the von Neumman entropy, majorization relations, and fidelity.
• The relevance to Zamolodchikov's c theorem is indicated.