Lattice models for non-Fermi liquids with tunable transport scalings

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 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 $\ensuremath{\varrho}\ensuremath{\sim}{T}^{\ensuremath{\alpha}}$ in a finite-temperature window, and $\ensuremath{\alpha}\ensuremath{\in}[1,2)$ depends on the fermion density in the model, which is a rather universal feature observed in many experimental systems.