The pseudo-gap phase and the duality in holographic fermionic system with dipole coupling on Q-lattice

We classify the different phases by the "pole-zero mechanism" for a holographic fermionic system which contains a dipole coupling with strength $p$ on a Q-lattice background. A complete phase structure in $p$ space can be depicted in terms of Fermi liquid, non-Fermi liquid, Mott phase and pseudo-gap phase. In particular, we find that in general the region of the pseudo-gap phase in $p$ space is suppressed when the Q-lattice background is dual to a deep insulating phase, while for an anisotropic background, we have an anisotropic region for the pseudo-gap phase in $p$ space as well. In addition, we find that the duality between zeros and poles always exists regardless of whether or not the model is isotropic.