The analytical treatments on the low energy behaviors of the holographic non-relativistic fermions

We investigate the low energy behaviors around the Fermi surface at the non-relativistic fixed points and give some clear and direct numerical results on the structure of the Fermi surface in the presence of a holographic flat band. Compared with the case of the dual relativistic fermionic system, the Fermi momentum is suppressed by the presence of the holographic flat band. In particular, we give an analytical understanding of the low energy behaviors of the dual non-relativistic fermionic system. One finds that due to AdS2×R2 background geometry in the near horizon limit, the scaling behaviors of the spectral function at the non-relativistic fixed points is as same as that at the relativistic fixed points, which controlled by the IR Greenʼs function GI(k,ω). As a check, we also give a comparison about the scaling exponents δ of the dispersion relation between the numerical and analytical results. One finds that the numerical result is agree well with the analytical that.