  A variety of exotic non-fermi liquid (NFL) states have been observed in many
condensed matter systems, with different scaling relations between transport
coefficients and temperature. The "standard" approach to studying these NFLs is
by coupling a Fermi liquid to quantum critical fluctuations, which potentially
can drive the system into a NFL. In this work we seek for an alternative
understanding of these various NFLs in a unified framework. We first construct
two "elementary" randomness-free models with four-fermion interactions only,
whose many properties can be analyzed exactly in certain limit just like the
Sachdev-Ye-Kitaev (SYK) model. The most important new feature of our models is
that, the fermion scaling dimension in the conformal invariant solution in the
infrared limit is tunable by charge density. Then based on these elementary
models, we propose two versions of lattice models with four fermion
interactions which give us non-fermi liquid behaviors with DC resistivity
scaling $\varrho \sim T^\alpha$ in a finite temperature window, and $\alpha \in
[1, 2)$ depends on the fermion density in the model, which is a rather
universal feature observed in many experimental systems.
