Holographic Lieb lattice and gapping its Dirac band

Abstract

We first point out that the Laia-Tong model realizes the Lieb lattice in the holographic setup. It generates a flat band of sharp particle spectrum together with a Dirac band of unparticle spectrum. We provided an understanding why the Laia-Tong model’s boundary condition generate a flat band and compared it with the mechanism of “compact localized orbits” in the lattice models to provide a physical reason why Lieb and Laia-Tong model should be identified based on the similarity in the flat band generation mechanism. We then construct a model which opens a gap to the Dirac band so that one can realize a well-separated flat band. We then study the phase transition between the gapped and gapless phases analytically. We also made methodological progress to find a few other possible quantizations and we express the Green functions in any quantization in terms of that in the standard quantization. Finally we carried out the problem of back reaction to show that the qualitative feature remains the same.