Flow equations for the ionic Hubbard model

Abstract

Taking the site-diagonal terms of the ionic Hubbard model (IHM) in one and two spatial dimensions, as H 0 , we employ Continuous Unitary Transformations (CUT) to obtain a "classical" effective Hamiltonian in which hopping term has been renormalized to zero. For this Hamiltonian spin gap and charge gap are calculated at half-filling and subject to periodic boundary conditions. Our calculations indicate two transition points. In fixed , as U increases from zero, there is a region in which both spin gap and charge gap are positive and identical; characteristic of band insulators. Upon further increasing U , first transition occurs at U = U c 1 , where spin and charge gaps both vanish and remain zero up to U = U c 2 . A gap-less state in charge and spin sectors characterizes a metal. For U > U c 2 spin gap remains zero and charge gap becomes positive. This third region corresponds to a Mott insulator in which charge excitations are gaped, while spin excitations remain gap-less.

Phase transitions in the binary-alloy Hubbard model: Insights from strong-coupling perturbation theory

“…Then at half-filling, a competition between ∆ and U will generate a conducting phase for ∆ ≈ U/2 within strong-coupling perturbation theory [7]. Similar picture is obtained by DMFT [9,13] and continuous unitary transformation (CUT) [40,41]. So the metallic phase, in this case, can be considered a descendant of the conducting phase in the above studies.…”

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

“…Now we can calculate the Green's function by substituting self-energy into Eq. (7). In order to monitor the Mott transition, we should calculate the DOS ρ(ω) = − 1 π lim η→0 + k Im Tr G(k, ω + iη) at different interaction strength.…”

“…In the large U limit again we have the Mott phase. When the Hubbard U is negligible in comparison to ∆, its main effect is to renormalize Fermi liquid parameters of the underlying metallic state, and hence the relevant parameter ∆ opens up a single-particle gap and we have a band insulator 7 . For the intermediate regime our earlier dynamical mean field theory (DMFT) study suggests the presence of a gapless semimetallic state which is born out of the competition between the two parameters U and ∆ 8,9 .…”

Classical analogue of the ionic Hubbard model

“…We have taken the example of the (IHM) [6,7]. This model was introduced to study the neutral-to-ionic transition in organic compounds, as well as, understanding the role of strong electronic correlations in the dielectric properties of metal oxides [7,8]. This model is as follows: where c iσ (c † iσ ) is the usual annihilation (creation) operator at site i with spin σ. U is the on-site Coulomb interaction parameter, and ∆ denotes a one-body staggered ionic potential.…”