Non-Ginzburg-Landau Type Universality in Quantum Metamagnetism Induced by Topological Change of Fermi Surface: Applications to a Weak Itinerant-Electron Ferromagnet ZrZn$_{2}$*

We clarify that metamagnetic transitions show unconventional properties as quantum phase transitions if they are accompanied by changes in Fermi-surface topology. Topological change of the Fermi surface makes the phase diagram qualitatively different from that of the conventional metamagnetic transitions; the quantum critical endpoint becomes not only the terminal of the finite-temperature critical line, but also the terminal of a quantum critical line of continuous Lifshitz transitions. Around the \textit{quantum critical terminal}, power-law singularities of thermodynamic quantities are determined by the Fermi-surface topology and, therefore, are characterized \textit{neither} by the Ising symmetry breaking \textit{nor} by the Ginzburg-Landau-Wilson scheme proposed by Moriya, Hertz and Millis for the conventional quantum criticalities. We propose that such an unconventional universality indeed accounts for the metamagnetic transitions observed in ZrZn$_{2}$.