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IOP Conference Series Materials Science and Engineering

Occupancy Fluctuation Effects on 3D Hubbard Model at Quarter Filling within Dynamical Mean-Field Theory

N. A. Tadjuddin, Choirun Nisaa Rangkuti, Muhammad Aziz Majidi

Published Apr 17, 2019• 0 citations
Publisher

Abstract

Research on materials classified into strongly-correlated systems has become a crucial subject due to the strong interactions among the material constituents yielding various exotic physical properties and phenomena. There have been many computational methods developed to address the properties of such systems accurately within the Hubbard model, but most of them require a lot of computational costs to expect good results. In this research, we proposed a new approach within the Dynamical Mean Field Theory (DMFT) framework that requires a simpler and potentially less numerical-cost algorithm. We implemented this algorithm by constructing the local self-energy matrix elements that depend on the occupancy fluctuations. We integrated them over all possible occupancy configurations to obtain the fully interacting Green functions. The resulted Green function matrix was then used to compute the density of states (DOS) and other quantities. We investigated the case of quarter filling. Our computation results showed that pseudogap appeared when the onsite Coulomb repulsion was sufficiently high and tended to diminish as temperature increased. The system preserved its paramagnetic metallic character for all circumstances we studied.

DOI
10.1088/1757-899x/515/1/012011

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Research on materials classified into strongly-correlated systems has become a crucial subject due to the strong interactions among the material constituents yielding various exotic physical properties and phenomena. There have been many computational methods developed to address the properties of such systems accurately within the Hubbard model, but most of them require a lot of computational costs to expect good results. In this research, we proposed a new approach within the Dynamical Mean Field Theory (DMFT) framework that requires a simpler and potentially less numerical-cost algorithm. We implemented this algorithm by constructing the local self-energy matrix elements that depend on the occupancy fluctuations. We integrated them over all possible occupancy configurations to obtain the fully interacting Green functions. The resulted Green function matrix was then used to compute the density of states (DOS) and other quantities. We investigated the case of quarter filling. Our computation results showed that pseudogap appeared when the onsite Coulomb repulsion was sufficiently high and tended to diminish as temperature increased. The system preserved its paramagnetic metallic character for all circumstances we studied.
Dynamical Mean-Field Theory (DMFT) is among the most widely used techniques in computational condensed-matter physics, especially in addressing electron-electron interactions. In this regard, Quantum Monte Carlo may be considered as the most accurate DMFT impurity solver, but it usually requires a high numerical cost. On the contrary, lower numerical-cost technique, such as mean-field theory, often gives inaccurate results due to complete suppression of quantum fluctuations. In this study, we propose a new potentially low numerical-cost impurity solver taking a full account of fluctuation effects. Applying this new algorithm on Hubbard model, we formulate local self-energy that depends on the occupancy fluctuations. These fluctuations act as the semi-classical degree of freedom that needs to be integrated to obtain the averaged fully interacting Green functions. We test our algorithm by addressing temperature dependence of the density of states that reveals metal-insulator transition.
The influence of disorder and pseudogap fluctuations on the Mott insulator-metal transition in strongly correlated systems has been studied in the framework of the generalized dynamic mean field theory (DMFT + Σ approach). Using the results of investigations of the density of states (DOS) and optical conductivity, a phase diagram (disorder-Hubbard interaction-temperature) is constructed for the paramagnetic Anderson-Hubbard model, which allows both the effects of strong electron correlations and the influence of strong disorder to be considered. Strong correlations are described using the DMFT, while a strong disorder is described using a generalized self-consistent theory of localization. The DOS and optical conductivity of the paramagnetic Hubbard model have been studied in a pseudogap state caused by antiferromagnetic spin (or charge) short-range order fluctuations with a finite correlation length, which have been modeled by a static Gaussian random field. The effect of a pseudogap on the Mott insulator-metal transition has been studied. It is established that, in both cases, the static Gaussian random field (related to the disorder or pseudogap fluctuations) leads to suppression of the Mott transition, broadening of the coexistence region of the insulator and metal phases, and an increase in the critical temperature at which the coexistence region disappears.
Abstract In this work for an interacting electrons system that obeys the Hubbard model, a new quantum Monte Carlo algorithm introduces for calculation of average Green function. This algorithm is applied to investigate the effects of electrons onsite Coulomb repulsion on the band structure of a square lattice in both single-site approximations such as dynamical mean field theory (DMFT) and multi-site approximations such as effective medium supercell approximation (EMSCA). The advantages of our algorithm in comparison to the Hirsch-Fye algorithm and also the Blankenbecler, Scalapino, and Sugar (BSS) algorithm are the elimination of instabilities resulting from the Metropolis algorithm in the accepting and rejecting configurations, stability at low temperatures, the elimination of systematic errors resulting from the update of the Green's function in the quantum Monte Carlo process, and considering different probabilities for each possible configuration. Finally, by using our algorithm, it is possible to calculate the interacting three-dimensional system's band structure and the density of states that obey the Hubbard model. We have applied our algorithm to an interactive two-dimensional square lattice. As a result, phase transition boundaries can be easily recognized through calculated bands for different repulsions. Our results show that critical Coulomb repulsion values for Mott transition are uc=9.05t and uc=2.4t for DMFT and BEMSCA respectively. This means that DMFT significantly overestimates band splitting due to electrons' Coulomb repulsion. We found by starting at low repulsions and then increasing electrons' Coulomb repulsion, a partially flatted valance band around the center of the first Brillouin zone appears, but disappears at high repulsions.
We generalize the dynamical-mean field (DMFT) approximation by including into the DMFT equations some length scale $\ensuremath{\xi}$ via a momentum dependent external self-energy ${\ensuremath{\Sigma}}_{\mathbf{k}}$. This external self-energy describes nonlocal dynamical correlations induced by the short-ranged collective spin density wave--like antiferromagnetic spin (or the charge density wave--like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with a finite correlation length. This generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with the nearest and the next nearest neighbor hopping. The effective single impurity problem in this generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ is solved by the numerical renormalization group. Both types of the strongly correlated metals, namely: (i) The doped Mott insulator and (ii) the case of the bandwidth $W\ensuremath{\lesssim}U$ (UUU---value of the local Coulomb interaction) are considered. The densities of states, the spectral functions, and the angle resolved photoemission spectra calculated within the $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ show a pseudogap formation near the Fermi level of the quasiparticle band.
Pseudogap physics in strongly correlated systems is essentially scale dependent. We generalize the dynamical mean field theory (DMFT) by including into the DMFT equations dependence on correlation length of pseudogap fluctuations via additional (momentum dependent) self-energy Sigma_k. This self-energy describes non-local dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT+Sigma_k approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with nearest and next nearest neighbour hopping. The effective single impurity problem is solved by numerical renormalization group (NRG). Both types of strongly correlated metals, namely (i) doped Mott insulator and (ii) the case of bandwidth W
We study the paramagnetic Anderson-Hubbard model using an extension of dynamical mean field theory (DMFT), known as statistical DMFT, that allows us to treat disorder and strong electronic correlations on equal footing. An approximate nonlocal Green's function is found for individual disorder realizations and then configuration averaged. We apply this method to two-dimensional lattices with up to 1000 sites in the strong disorder limit, where an atomic-limit approximation is made for the self-energy. We investigate the scaling of the inverse participation ratio at quarter- and half-filling, and find a nonmonotonic dependence of the localization length on the interaction strength. For strong disorder, we do not find evidence for an insulator-metal transition, and the disorder potential becomes unscreened near the Mott transition. Furthermore, strong correlations suppress the Altshuler-Aronov density of states anomaly near half-filling.