  Strange metal behavior is traditionally associated with an underlying
putative quantum critical point at zero temperature. However, in many
correlated metals, e.g., high-Tc cuprate superconductors, strange metallicity
persists at low temperatures over an extended range of microscopic parameters,
suggesting the existence of an underlying quantum critical phase, whose
possible physical origins remain poorly understood. Systematic investigations
of physical scenarios giving rise to such a critical, non-Fermi liquid (NFL)
phase are therefore crucial to better understand this puzzling behavior. In a
previous work [Bashan et al. arXiv:2310.07768], we considered a solvable
large-N model consisting of itinerant electrons coupled to local two-level
systems (TLSs) via spatially random interactions, inspired by the possibility
of emergent metallic glassiness due to frustrated competing orders, and found
that the system hosts an NFL phase with tunable exponents at intermediate
couplings. In this work, we expand our investigation to the following: (i) We
study the extent to which this NFL phase is generic by considering various
deformations of our theory, including coupling of electrons to multiple
operators of the TLSs and arbitrarily directed TLS-fields. We find that the
physical picture obtained in Bashan et al. qualitatively persist in a wide
region of parameter space, showcasing the robustness of the NFL phase; (ii) We
analyze the superconducting instability due to coupling of TLSs to electrons,
and find a rich structure, including quantum critical pairing associated with
the NFL phase and conventional BCS pairing in the weak and strong coupling
limits; (iii) We elaborate on the analysis of Bashan et al., including
single-particle, transport and thermodynamic properties.
