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We study a model of strongly-correlated systems that incorporates phases suchas Fermi liquids, non-Fermi liquids, and superconductivity, in addition topotential intertwined orders. The model describes Fermi surfaces of spinfulelectron gas or electron liquid coupled to bosons via an intermediate gaugefield. Effectively, the coupling imposes constraints and interactions betweenthe fermion spin and the local boson density. This grants the bosons themeaning as the Schwinger boson of the magnetic order and allows us to probe alarger phase space, rather than around the quantum critical point. We designthe initial model so that after the boson and gauge fields are integrated outexactly, the resulting fermion-only effective theory only consists of severallocal interactions, allowing controlled weak-coupling interpretation forcertain parameter regions. Consequently, we find a non-Fermi liquid whosedegrees of freedom in the effective theory take the form of an \emph{emergent}Fermi surface that has a different Luttinger volume from the original fermions,therefore explicitly violates the Luttinger theorem. Further, this allows a$d$-wave superconducting instability if the effective interacting induced byboson coupling is in the relevant pairing channel. When the emergent Fermisurface undergoes a Lifshitz transition, the carrier type changes. In addition,we attribute the Mott insulating behavior in the strong coupling limit to theloss of emergent Fermi surface and argue the possibility of coexisting magneticorder. Our effective theory also suggests the possibility of charge densitywaves as a consequence of \emph{effective} strong repulsion and is independentof the Fermi-surface-nesting scenario. We discuss the possible optimalconditions for higher superconducting transition temperature and potentialrelevances and implications for realistic materials.

Unified non-Fermi liquid and superconductivity in a model of strongly-correlated systems