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We address the nature of the Mott transition in the Hubbard model at half-filling using cluster Dynamical Mean Field Theory (DMFT). We compare cluster DMFT results with those of single site DMFT. We show that inclusion of the short range correlations on top of the on-site correlations, already treated exactly in single site DMFT, do not change the nature of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical $U$ and modify the shape of transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition, in particular in the region of the phase diagram where the two solutions coexist. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale at temperatures as low as $T=0.01t$. The insulating state is characterized by the relatively narrow Mott gap with pronounced peaks at the gap edge.
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The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.
We describe the use of coupled-cluster theory as an impurity solver in dynamical mean-field theory (DMFT) and its cluster extensions. We present numerical results at the level of coupled-cluster theory with single and double excitations (CCSD) for the density of states and self-energies of cluster impurity problems in the one- and two-dimensional Hubbard models. Comparison to exact diagonalization shows that CCSD produces accurate density of states and self-energies at a variety of values of $U/t$ and filling fractions. However, the low cost allows for the use of many bath sites, which we define by a discretization of the hybridization directly on the real frequency axis. We observe convergence of dynamical quantities using approximately 30 bath sites per impurity site, with our largest 4-site cluster DMFT calculation using 120 bath sites. We suggest coupled cluster impurity solvers will be attractive in ab initio formulations of dynamical mean-field theory.
We examine the cluster-size dependence of the cellular dynamical mean-field theory (CDMFT) applied to the two-dimensional Hubbard model. Employing the continuous-time quantum Monte Carlo method as the solver for the effective cluster model, we obtain CDMFT solutions for 4-, 8-, 12-, and 16-site clusters at a low temperature. Comparing various periodization schemes, which are used to construct the infinite-lattice quantities from the cluster results, we find that the cumulant periodization yields the fastest convergence for the hole-doped Mott insulator where the most severe size dependence is expected. We also find that the convergence is much faster around (0,0) and (pi/2,pi/2) than around (pi,0) and (pi,pi). The cumulant-periodized self-energy seems to be close to its thermodynamic limit already for a 16-site cluster in the range of parameters studied. The 4-site results remarkably agree well with the 16-site results, indicating that the previous studies based on the 4-site cluster capture the essence of the physics of doped Mott insulators.
We discuss some aspects of the pressure (or interaction) driven Mott transition, in three dimensional transition metal oxides by means of dynami cal mean field theory. We isolate the universal properties of the transition from the aspects which depend more on the detailed chemistry of the compounds. In this light we can understand the main differences and the remarkable similarities between these systems. Both theory and experiment converge on the transfer of spectral weight from low energies to high energies as the universal mechanism underlying the Mott transition, and we comment on the possible relevance of these ideas to other metal to non metal transitions.
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.
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