The metal–insulator transition in the paramagnetic Hubbard Model

We apply a recently introduced hybridization-flow functional renormalization group scheme for Anderson-like impurity models as an impurity solver in a dynamical mean-field theory (DMFT) approach to lattice Hubbard models. We present how this scheme is capable of reproducing metallic and insulating solutions of the lattice model. Our setup also offers a numerically rather inexpensive method to calculate two-particle correlation functions. For the paramagnetic Hubbard-model on the Bethe lattice in infinite dimensions we calculate the local two-particle-vertex for the metallic and the insulating phase. Then we go to a two-site cluster-DMFT-scheme for the two-dimensional Hubbard-model that includes short-range antiferromagnetic fluctuations and obtain the local and non-local two-particle-vertex-functions. We discuss the rich frequency structures of these vertices and compare with the vertex in the single-site solution.

A cellular dynamical mean field theory approach to Mottness

A new numerical method for the solution of the dynamical mean field theory's self-consistent equations is introduced. The method uses the density matrix renormalization group technique to solve the associated impurity problem. The new algorithm makes no a priori approximations and is only limited by the number of sites that can be considered. We obtain accurate estimates of the critical values of the metal-insulator transitions and provide evidence of substructure in the Hubbard bands of the correlated metal. With this algorithm, more complex models having a larger number of degrees of freedom can be considered and finite-size effects can be minimized.

Metal-insulator transition in correlated systems: A new numerical approach

We report a study of metal-insulator transition of a strongly correlated two-band Hubbard model using a dynamical mean-field theory approach. We find that the Mott transition appears at half filling even at $T=0$ in contrast to the one-band Hubbard model. The transition is characterized by the development of a ``Kondo-like'' peak near Fermi level. We also find a signature of the coexistence of metallic and antiferromagnetic phases from the study of the single-particle Green's function and the magnetic long-range order due to the superexchange coupling between the correlated electrons. We then suggest the relevance of our results to the metal-insulator transition and the recent angle-resolved photoemission measurements of ${\mathrm{NiS}}_{2\ensuremath{-}x}{\mathrm{Se}}_{x}.$ We also study the effect of carrier doping and the comparison of our findings with the experimental results suggests the possible importance of departures from stoichiometry associated with the Se substitution. The relevance of our results to high-temperature superconductivity is also discussed.

The metal-insulator transition (MIT) remains among the most thoroughly studied phenomena in solid state physics, but the complexity of the phenomena, which usually involves cooperation of many degrees of freedom including orbitals, fluctuating local moments, magnetism, and the crystal structure, have resisted predictive ab-initio treatment. Here we develop ab-initio theoretical method for correlated electron materials, based on Dynamical Mean Field Theory, which can predict the change of the crystal structure across the MIT at finite temperature. This allows us to study the coupling between electronic, magnetic and orbital degrees of freedom with the crystal structure across the MIT in rare-earth nickelates. We predict the electronic free energy profile of the competing states, and the theoretical magnetic ground state configuration, which is in agreement with neutron scattering data, but is different from the magnetic models proposed before. The resonant elastic X-ray response at the K-edge, which was argued to be a probe of the charge order, is theoretically modelled within the Dynamical Mean Field Theory, including the core-hole interaction. We show that the line-shape of the measured resonant elastic X-ray response can be explained with the “site-selective” Mott scenario without real charge order on Ni sites.

The cluster perturbation theory is presented in the 2D Hubbard model constructed using X operators in the Hubbard-I approximation. The short-range magnetic order is taken into account by dividing the entire lattice into individual 2 × 2 clusters and solving the eigenvalue problem in an individual cluster using exact diagonalization taking into account all excited levels. The case of half-filling taking into account jumps between nearest neighbors is considered. As a result of numerical solution, a shadow zone is discovered in the quasiparticle spectrum. It is also found that a gap in the density of states in the quasiparticle spectrum at zero temperature exists for indefinitely small values of Coulomb repulsion parameter U and increases with this parameter. It is found that the presence of this gap in the spectrum is due to the formation of a short-range antiferromagnetic order. An analysis of the temperature evolution of the density of states shows that the metal-insulator transition occurs continuously. The existence of two characteristic energy scales at finite temperatures is demonstrated, the larger scale is associated with the formation of a pseudogap in the vicinity of the Fermi level, and the smaller scale is associated with the metal-insulator transition temperature. A peak in the density of states at the Fermi level, which is predicted in the dynamic mean field theory in the vicinity of the metal-insulator transition, is not observed.

formula omitted]QIST v0.7: An open source continuous-time quantum Monte Carlo impurity solver toolkit

The evolution of the properties of a finite density electronic system as a function of the electron-phonon coupling is investigated in the Holstein model using the dynamical mean-field theory (DMFT) that becomes exact in infinite dimensions. We compare the spinless fermion case, in which only isolated polarons can be formed, with the spinful model in which the polarons can bind and form bipolarons. In the latter case, the bipolaronic binding occurs within DMFT as a metal-insulator transition. In the adiabatic regime in which the phonon energy is small with respect to the electron hopping we compare numerically exact DMFT results with an analytical scheme inspired by the Born-Oppenheimer procedure. Within the latter approach, a truncation of the phononic Hilbert space leads to a mapping of the original model onto an Anderson spin-fermion model. In the anti-adiabatic regime (where the phonon energy exceeds the electronic scales) the standard treatment based on Lang-Firsov canonical transformation allows one to map the original model on to an attractive Hubbard model in the spinful case. The separate analysis of the two regimes supports the numerical evidence that the presence of well-defined polaronic lattice displacements is not necessarily associated to a metal-insulator transition, which is instead due to pairing between the carriers. The finite-dimensionality effects neglected in DMFT may lead to a finite conductivity in the bipolaronic state which is, however, not always associated with polaronic distortions. At the polaron crossover the Born-Oppenheimer approximation is shown to break down due to the entanglement of the electron-phonon state.

Intermediate configurations in the plutonium and iron perovskite compound PuFeO3 are investigated using a combined density functional theory plus dynamical mean-field theory (DFT + DMFT) approach. Our findings reveal orbital-selective metal-insulator transitions driven by spin-orbit split Pu-5f states. Itinerant 5f5/2 electrons exhibit correlated metallic behavior, while localized 5f7/2 states display Mott-insulating characteristics. We report an average 5f occupancy of 4.649, suggesting intermediate valence states. Quantum mechanical analysis highlights the Pu-5f/Fe-3d hybridization, confirmed by the orbital-resolved self-energy and spectral function calculations. This study provides new insights into the electronic structure and bonding mechanisms of Pu-based perovskites, advancing the understanding of strongly correlated actinide materials.

Iron oxide is one of the most important components in the Earth’s mantle. The recent discovery of the stable presence of Fe5O6 in the Earth’s mantle environment has stimulated significant interests in understanding of this new category of iron oxides. We report the electronic structure and magnetic properties of Fe5O6 calculated by the density functional theory plus dynamic mean field theory (DFT + DMFT) approach. Our calculations indicate that Fe5O6 is a conductor at ambient pressure with dominant Fe-3d density of states at the Fermi level. The magnetic moments of iron atoms at three non-equivalent crystallographic sites in Fe5O6 collapse at significantly different rates under pressure. This site-selective collapse of magnetic moments originates from the shifting of energy levels and the consequent charge transfer among the Fe-3d orbits when Fe5O6 is being compressed. Our simulations suggest that there could be high conductivity and volume contraction in Fe5O6 at high pressure, which may induce anomalous features in seismic velocity, energy exchange, and mass distribution in the deep interior of the Earth.

The electronic structure of the rare-earth mononitrides LnN (where Ln = rare-earth), which are promising materials for future spintronics applications, is difficult to resolve experimentally due to a strong influence of defects on their transport and optical properties. At the same time, LnN are challenging for theory, since wide semiconducting 2p and 5d bands need to be described simultaneously with strongly correlated 4f states. Here, we calculate the many-body spectral functions and optical gaps of a series of LnN (with Ln = Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er) by a density-functional + dynamical mean-field theory (DFT + DMFT) approach treating the correlated Ln 4f shells within the quasi-atomic Hubbard-I approximation. The on-site Coulomb interaction in the 4f shell is evaluated by a constrained DFT + Hubbard-I approach. Furthermore, to improve the treatment of semiconducting bands in DFT + DMFT, we employ the modified Becke–Johnson semilocal exchange potential. Focusing on the paramagnetic high-temperature phase, we find that all investigated LnN are pd semiconductors with gap values ranging from 1.02 to 2.14 eV along the series. The pd band gap is direct for light Ln = La…Sm and becomes indirect for heavy rare-earths. Despite a pronounced evolution of the Ln 4f states along the series, empty 4f states are invariably found above the bottom of the 5d conduction band. The calculated spectra agree well with those available from x-ray photoemission, x-ray emission and x-ray absorption measurements.

We consider the interaction-driven Mott transition at zero temperature from the viewpoint of microscopic Fermi liquid theory. To this end, we derive an exact expression for the Landau parameters within the dynamical mean-field theory (DMFT) approximation to the single-band Hubbard model. At the Mott transition the symmetric and the anti-symmetric Landau parameter diverge. The vanishing compressibility at the Mott transition directly implies the divergence of the forward scattering amplitude in the charge sector, which connects the proximity of the Mott phase to a tendency towards phase separation. We verify the expected behavior of the Landau parameters in a DMFT application to the Hubbard model on the triangular lattice at finite temperature. Exact conservation laws and the Ward identity are crucial to capture vertex divergences related to the Mott transition. We furthermore generalize Leggett's formula for the static susceptibility of the Fermi liquid to the static fermion-boson response function. In the charge sector the limits of small transferred momentum and frequency of this response function commute at the Mott transition.

A review of the present state of investigations of the pseudospin-electron model (PEM), which is used in the theory of strongly correlated electron systems, is given. The model is used to describe the systems with the locally anharmonic elements of structure represented in the model by pseudospins. The consideration is based on the dynamical mean field theory approach and the generalized random phase approximation. Electron spectrum and thermodynamics of the model are investigated; the cases of the simplified model, the model with strong interaction and the two-sublattice model are studied more in detail. The phase transitions into other uniform or modulated states as well as superconducting phases are described; the criteria of their realization are established. Based on this, the description of structural and dielectric (ferroelectric type) instabilities, phase separation and bistability phenomena is given. A comparison is made with the thermodynamics of the Falicov-Kimball model (which can be considered as a particular case of PEM). The possibility of applying the PEM to the analysis of thermodynamics of the real HTSC systems is discussed. Attention is paid to the unsolved problems in the study of PEM.

An acceleration of continuous time quantum Monte Carlo (CTQMC) methods is a potentially interesting branch of work as they are matchless as impurity solvers of a density functional theory in combination with a dynamical mean field theory approach for the description of electronic structures of strongly correlated materials. The inversion of the $k \times k$ matrix given by the diagram expansion order $k$ in the CTQMC update and the multiplication of the $k \times k$ matrix and the non-interacting Green's function to measure the impurity Green's function are computationally time-consuming. Here, we propose the CTQMC method in combination with a machine learning technique, which would eliminate the need for multiplication of the matrix with the non-interacting Green's function. This method predicts the accurate impurity Green's function and double occupancy at low temperature, and also considers the physical properties of high Matsubara frequency in a much shorter computational time than the conventional CTQMC method.