Non-Laudau Quantum Phase Transitions and Nearly-Marginal Fermi Liquid*

Marginal fermi liquid and quantum critical points (QCP) with strong fractionalization are two exceptional phenomena beyond the classic condensed matter doctrines, which could occur in strongly interacting quantum many-body systems. This work demonstrates that these two phenomena may be tightly connected. To elaborate this connection, we propose a physical mechanism for "nearly-marginal Fermi liquid", namely the fermion self-energy scales as Σ_f(iω)~i sgn(ω)|ω|^α with α close to 1 in a considerable energy window. The nearly-marginal fermi liquid is obtained by coupling an electron fermi surface to unconventional QCPs that are beyond the Landau's paradigm. This mechanism relies on the observation that the anomalous dimension η of the order parameter of these unconventional QCPs can be close to 1, which is significantly larger than conventional Laudau phase transitions. The fact that η~1 justifies a controlled perturbative renormalization group expansion proposed previously. Candidate QCPs that meet this desired condition are proposed.