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.