Understanding non-Fermi liquids in dimensions higher than one has been a subject of great interest. Such phases may serve as parent states for other unconventional phases of quantum matter, in a similar manner that conventional broken symmetry states can be understood as instabilities of the Fermi liquid. In this work, we investigate the emergence of an exotic non-Fermi liquid in two dimensions, where the fermions with quadratic band-touching dispersion interact with Bose metal. The bosonic excitations in Bose metal possess an extended nodal-line spectrum in momentum space, which arises due to the subsystem symmetry or the restricted motion of bosons. Using renormalization group analysis and direct computations, we show that the extended infrared singularity of Bose metal leads to a line of interacting fixed points of an exotic non-Fermi liquids, where the anomalous dimension of the fermions varies continuously, akin to the Luttinger liquid in one dimension. Further, the generalization of the model with multiple low-energy excitations is used to explore other unusual features of the resulting ground state.

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• Strongly correlated systems
• Non-Fermi-liquid theory
• Renormalization group