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

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 Uc ≈ 2.38t. 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, ∆. The present approach gives a critical gapless state at U = 2∆ at lowest order. By systematically improving on the perturbation expansion, the density of states around this critical gapless phase reduces.

Quantum Integrability of 1D Ionic Hubbard Model

“…Furthermore, panel (d) is very similar to panel (b) that corresponds to a pure band insulator. The OPDM spectrum suggests that at half‐filling, as long as , the ground state can be regarded as a renormalized band‐insulator . Classically the energy 2Δ is the ionic barrier that prevents the Hubbard U from excluding the double occupancy.…”

Electronic properties of the Dirac and Weyl systems with first- and higher-order dispersion in non-Fermi-liquid picture

“…where ψ is the Fermion field and φ is the Bosonic field which describes the long-range instantaneous Coulomb interaction and related to the order parameter, and the Fermions couples to the Bosons through the coupling constant g 2 = 2πe 2 /ǫ > 0 where ǫ is the background dielectric constant. Here we focus on the long-range Coulomb interaction, while for the doped case with strong fluctuation[], the strong attraction within the short-range pairs may induces the Mott insulator phase [27,28] or the superconductivity order parameter at finite doping [1]. The H 0 (k) is the non-interacting Hamiltonian which for 2D linear Dirac system reads…”

Semiconductor of spinons: from Ising band insulator to orthogonal band insulator

“…Starting from massive Dirac fermions on the honeycomb lattice the competition between U and the single-particle gap parameter ∆ (known as mass term when it comes to Dirac fermions) gives rise to massless Dirac fermions [27]. A recent strong coupling expansion gives a quantum critical semi-metallic state [7].…”

“…The canonical model within which the metal-to-insulator transition (MIT) problem is investigated is the Hubbard model [2]. Efforts to understand the nature of MIT has lead to many technical [3][4][5][6][7][8][9][10][11][12][13][14] and conceptual [15][16][17][18][19] developments providing clues into possible mechanisms of non-Fermi liquid formation.But even more challenging question is what happens when both mechanisms of gap formation are simultaneously present, i.e. what are the properties of strongly correlated band insulators or semiconductors?…”

“…Starting from massive Dirac arXiv:1601.02108v3 [cond-mat.str-el] 29 Jul 2016 2 fermions on the honeycomb lattice the competition between U and the single-particle gap parameter ∆ (known as mass term when it comes to Dirac fermions) gives rise to massless Dirac fermions [27]. A recent strong coupling expansion gives a quantum critical semi-metallic state [7].When electron correlations in a conductor are not strong enough to transform the metallic state to a Mott insulator, they give rise to possible non-Fermi liquid states. From this point of view one may now turn on the ionic potential ∆ and ask the following question: How does this staggered potential interfere with possible non-Fermi liquid state of the parent metal?…”