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We compare the roles of fidelity and entanglement in characterizingrenormalization group flows and quantum phase transitions. It turns out thatthe scaling parameter extracted from fidelity for different ground statessucceeds to capture nontrivial information including stable and unstable fixedpoints, whereas the von Neumann entropy as a bipartite entanglement measure (orequivalently, majorization relations satisfied by the spectra of the reduceddensity matrix along renormalization group flows) often fails, as far as theintrinsic irreversibility-information loss along renormalization group flows-isconcerned. We also clarify an intimate connection between the von Neummanentropy, majorization relations, and fidelity. The relevance to Zamolodchikov'sc theorem is indicated.

Renormalization group flows and quantum phase transitions: fidelity versus entanglement