Holographic lattices and metal-insulator transition

This paper is an extension of the talk given at the conference on Gravitation and Cosmology/The Fourth Galileo-Xu Guangqi Meeting. We intend to present a short review on recent progress on the construction of holographic lattices and its application to metal-insulator transition (MIT), which is a fundamentally important phenomenon in condensed matter physics. We will firstly implement the Peierls phase transition by constructing holographic charge density waves which are induced by the spontaneous breaking of translational symmetry. Then we turn to the holographic realization of metal-insulator transition as a quantum critical phenomenon with many strongly correlated electrons involved. The holographic entanglement entropy as a diagnostic for such quantum phase transitions will be briefly mentioned.