Onset of charge incompressibility and Mott gaps in the Honeycomb-Lattice SU(4) Hubbard Model: Lessons for Twisted Bilayer Graphene systems

TL;DR

This study uses strong coupling expansions to analyze thermodynamic properties and the emergence of Mott gaps in the SU(4) Hubbard model on a honeycomb lattice, with implications for twisted bilayer graphene.

Contribution

It introduces a high temperature expansion approach for the SU(4) Hubbard model and discusses its relevance to twisted bilayer graphene systems.

Findings

Identification of charge incompressibility and Mott gap formation at low temperatures.

Validation of strong coupling expansions through convergence analysis.

Insights into high temperature behavior relevant to flat-band materials.

Abstract

We use finite temperature strong coupling expansions to calculate thermodynamic properties of the Honeycomb-lattice SU(4) Hubbard model. We present numerical results for various properties including chemical potential, compressibility, entropy and specific heat as a function of temperature and density at several $U/t$ values. We study the onset of charge incompressibility and Mott gaps as the temperature is lowered at integer densities. In the incompressible Mott regime, the expansions are recast into a high temperature expansion for a generalized spin model with SU(4) symmetry, which is then used to study the convergence of strong coupling expansions in t/U. We discuss lessons that can be drawn from high temperature properties of a simple Hubbard model regarding Twisted Bilayer Graphene (TBG) and other magic-angle flat-band systems.