Holographic Lieb lattice and gapping its Dirac band

TL;DR

This paper demonstrates how the Laia-Tong holographic model realizes a Lieb lattice with a flat band and Dirac spectrum, introduces a gap to study phase transitions, and advances methods to analyze Green functions in various quantizations.

Contribution

It constructs a holographic model that opens a gap in the Dirac band of the Lieb lattice, enabling the study of flat bands as strongly correlated system analogs, and develops methods for Green function analysis.

Findings

Realization of Lieb lattice in holography with flat and Dirac bands

Analytical study of phase transition between gapped and gapless phases

Methodological progress in expressing Green functions across quantizations

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 then construct a model which opens a gap to the Dirac band so that one can realize a well-separated flat band, which can play the role of the hydrogen atom of strongly correlated systems. We then study the phase transition between the gapped and gapless phases analytically. We also made methodological progress to find a few other quantizations and we express the Green functions in any quantization in terms of that in the standard quantization.