Multisite versus multiorbital Coulomb correlations studied within finite-temperature exact diagonalization dynamical mean-field theory

Abstract

The influence of short-range Coulomb correlations on the Mott transition in the single-band Hubbard model at half filling is studied within cellular dynamical mean-field theory for square and triangular lattices. Finitetemperature exact diagonalization is used to investigate correlations within two-, three-, and four-site clusters. Transforming the nonlocal self-energy from a site basis to a molecular-orbital basis, we focus on the interorbital charge transfer between these cluster molecular orbitals in the vicinity of the Mott transition. In all cases studied, the charge transfer is found to be small, indicating weak Coulomb-induced orbital polarization despite sizable level splitting between orbitals. These results demonstrate that all cluster molecular orbitals take part in the Mott transition and that the insulating gap opens simultaneously across the entire Fermi surface. Thus, at half filling we do not find orbital-selective Mott transitions or a combination of band filling and Mott transition in different orbitals. Nevertheless, the approach toward the transition differs greatly between cluster orbitals, giving rise to a pronounced momentum variation along the Fermi surface, in agreement with previous works. The near absence of Coulomb-induced orbital polarization in these clusters differs qualitatively from single-site multiorbital studies of several transition-metal oxides, where the Mott phase exhibits nearly complete orbital polarization as a result of a correlation driven enhancement of the crystal-field splitting. The strong singleparticle coupling among cluster orbitals in the single-band case is identified as the source of this difference.

Spectral properties of the three-dimensional Hubbard model

“…Previous studies of the interaction driven MH-MIT at non-zero temperature were largely performed on a Bethe lattice in the limit of infinite dimension within the DMFT approximation 58,59 , respectively for a twodimensional Hubbard model using the correlator projection method 17,19 or cluster DMFT 16,18,[20][21][22][23][24][25] . While the general features of the MH-MIT appear to be rather insensitive to the actual non-interacting band structure, the details like critical values for temperature and Coulomb interactions vary strongly with details of the model as well as the approximations involved in the computation and finite size effects.…”

Correlated Dirac fermions on the honeycomb lattice studied within cluster dynamical mean field theory

“…Evidently, there is little orbital polarization, a result that was also observed in CDMFT calculations for the square and triangular lattices. 21 Moreover, the double occupancy, the spin correlations, and the orbital occupancies reveal no clear sign of a Mott transition in the region where the spectral distribution exhibits the opening of a gap.…”

Geometrical frustration effects on charge-driven quantum phase transitions

“…22,23 The large number of excited states inherent to the many-body problem which are needed to evaluate statistical sums is cut off by keeping only a small number of low-lying states at each temperature. This is performed through an Arnoldi algorithm 24 which reduces the size of the Hilbert space enormously.…”

“…IV the resulting metallic phases are explored through a finite-T Lanczos diagonalization calculation. [22][23][24] We theoretically explore the consequences of a quantum critical point (QCP) at a charge-ordering transition driven by the quantum fluctuations associated with strong intersite Coulomb repulsion. Our results are compared with a spinless calculation in order to assess the importance of the magnetic degrees of freedom in the observed quantum criticality and make contact with the existing literature.…”