Strong coupling approach to Mott transition of massless and massive Dirac fermions on honeycomb lattice

TL;DR

This paper develops a strong coupling perturbation theory to analyze Mott transitions in honeycomb lattice models, providing precise critical values and insights into insulating states with potential for high-accuracy predictions.

Contribution

It introduces an analytic strong coupling approach for the Hubbard and ionic Hubbard models on honeycomb lattices, enabling precise determination of Mott transition points and insulating states.

Findings

Critical Mott transition at U_c ≈ 2.38 t

Identification of two insulating states in ionic Hubbard model

Critical gapless state at U=2Δ

Abstract

Phase transitions in the Hubbard model and ionic Hubbard model at half-filling on the honeycomb lattice are investigated in the strong coupling perturbation theory which corresponds to an expansion in powers of the hopping $t$ around the atomic limit. Within this formulation we find analytic expressions for the single-particle spectrum, whereby the calculation of the insulating gap is reduced to a simple root finding problem. This enables high precision determination of the insulating gap that does not require any extrapolation procedure. The critical value of Mott transition on the honeycomb lattice is obtained to be $U_c\approx 2.38 t$. Studying the ionic Hubbard model at the lowest order, we find two insulating states, one with Mott character at large $U$ and another with single-particle gap character at large ionic potential, $\Delta$. The present approach gives a critical gapless state at $U=2\Delta$ at lowest order. By systematically improving on the perturbation expansion, the density of states around this critical gapless phase reduces.