Infinite critical boson non-Fermi liquid

We study a distinct type of non-Fermi liquid where there exists an infinite number of critical bosonic modes instead of a finite number of bosonic modes for the conventional ones. We consider itinerant magnets with both conduction electrons and fluctuating magnetic moments in three dimensions. With the Dzyaloshinskii-Moriya interaction, the moments fluctuate near a boson surface in the reciprocal space at low energies when the system approaches an ordering transition. The infinite number of critical modes on the boson surface strongly scatter the gapless electrons on the Fermi surface and convert the metallic sector into a non-Fermi liquid. We explain the physical properties of this non-Fermi liquid. On the ordered side, a conventional non-Fermi liquid emerges due to the scattering by the gapless Goldstone mode from the spontaneous breaking of the global rotational symmetry. We discuss the general structure of the phase diagram in the vicinity of the quantum phase transition and clarify various crossover behaviors.