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Register a new userIntrinsic Cluster-Shaped Density Waves in Cellular Dynamical Mean-Field Theory
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It is well known that cellular dynamical mean-field theory (CDMFT) leads to the artificial breaking of translation invariance. In spite of this, it is one of the most successful methods to treat strongly correlated electrons systems. Here, we investigate in more detail how this broken translation invariance manifests itself. This allows to disentangle artificial broken translation invariance effects from the genuine strongly correlated effects captured by CDMFT. We report artificial density waves taking the shape of the cluster---cluster density waves---in all our zero temperature CDMFT solutions, including pair density waves in the superconducting state. We discuss the limitations of periodization regarding this phenomenon, and we present mean-field density-wave models that reproduce CDMFT results at low energy in the superconducting state. We then discuss how these artificial density waves help the agreement of CDMFT with high temperature superconducting cuprates regarding the low-energy spectrum, in particular for subgap structures observed in tunnelling microscopy. We relate these subgap structures to nodal and anti-nodal gaps in our results, similar to those observed in photoemission experiments. This fortuitous agreement suggests that spatial inhomogeneity may be a key ingredient to explain some features of the low-energy underdoped spectrum of cuprates with strongly correlated methods. This work deepens our understanding of CDMFT and clearly identifies signatures of broken translation invariance in the presence of strong correlations.
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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.
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 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.
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.
In this thesis we study the strongly-correlated-electron physics of the longstanding H-Tc-superconductivity problem using a non-perturbative method, the Dynamical Mean Field Theory (DMFT), capable to go beyond standard perturbation-theory techniques. DMFT is by construction a local theory which neglects spatial correlation. Experiments have however shown that the latter is a fundamental property of cuprate materials. In a first step, we approach the problem of spatial correlation in the normal state of cuprate materials using a phenomenological Fermi-Liquid-Boltzmann model. We then introduce and develop in detail an extension to DMFT, the Cellular Dynamical Mean Field Theory (CDMFT), capable of considering short-ranged spatial correlation in a system, and we implement it using the exact diagonalization algorithm . After benchmarking CDMFT with the exact one-dimensional solution of the Hubbard Model, we employ it to study the density-driven Mott metal-insulator transition in the two-dimensional Hubbard Model, focusing in particular on the anomalous properties of the doped normal state close to the Mott insulator. We finally study the superconducting state. We show that within CDMFT the one-band Hubbard Model supports a d-wave superconductive state, which strongly departs from the standard BCS theory. We conjecture a link between the instabilities found in the normal state and the onset of superconductivity.
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