Cluster Dynamical Mean Field Methods and the Momentum-selective Mott transition

Hung Dang, Xiao Yan Xu, Kuang-Shing Chen +2 more

David Sénéchal

Erik G. C. P. van Loon, Mikhail I. Katsnelson, Hartmut Hafermann

We apply the dual fermion approach with a second-order approximation to the self-energy to the Mott transition in the two-dimensional Hubbard model. The approximation captures nonlocal dynamical short-range correlations as well as several features observed in studies using cluster dynamical mean-field theory. This includes a strong reduction of the critical interaction and inversion of the slope of the transition lines with respect to single-site dynamical mean-field theory. We show that these effects coincide with a much smaller momentum differentiation compared to cluster methods. We further discuss the role of the self-consistency condition and show that the approximation behaves as an asymptotic series at low temperature.

Volodymyr Turkowski, James K. Freericks, V. Zlatić

A. Liebsch, H. Ishida, Jaime Merino

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. Finite-temperature 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 single-particle coupling among cluster orbitals in the single-band case is identified as the source of this difference.

Michel Ferrero, Pablo S. Cornaglia, Lorenzo De Leo +3 more

We introduce a valence bond dynamical mean-field theory of doped Mott insulators. It is based on a minimal cluster of two orbitals, each associated with a different region of momentum space and hybridized to a self-consistent bath. The low-doping regime is characterized by singlet formation and the suppression of quasiparticles in the antinodal regions, leading to the formation of Fermi arcs. This is described in terms of an orbital-selective transition in reciprocal space. The calculated tunneling and photoemission spectra are consistent with the phenomenology of the normal state of cuprates. We derive a low-energy description of these effects using a generalization of the slave-boson method.