Dynamical Mean-field Theory Research Articles

Superconductivity in the two-dimensional Hubbard model with cellular dynamical mean-field theory: A quantum impurity model analysis

Superconductivity in the two-dimensional Hubbard model with cellular dynamical mean-field theory: A quantum impurity model analysis

Heavy quasiparticles and cascades without symmetry breaking in twisted bilayer graphene

Among the variety of correlated states exhibited by twisted bilayer graphene, cascades in the spectroscopic properties and in the electronic compressibility occur over larger ranges of energy, twist angle and temperature compared to other effects. This suggests a hierarchy of phenomena. Using a combined dynamical mean-field theory and Hartree calculation, we show that the spectral weight reorganisation associated with the formation of local moments and heavy quasiparticles can explain the cascade of electronic resets without invoking symmetry breaking orders. The phenomena reproduced here include the cascade flow of spectral weight, the oscillations of remote band energies, and the asymmetric jumps of the inverse compressibility. We also predict a strong momentum differentiation in the incoherent spectral weight associated with the fragile topology of twisted bilayer graphene.

A new algorithm for investigating strongly correlated systems using Hubbard model

In this work, a new algorithm introduces for calculating the average Green function of an interacting system that obeys the Hubbard model. This algorithm is applied to investigate the effects of onsite repulsion on the band structure of a square lattice in both the 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 valence band around the center of the first Brillouin zone appears, but disappears at high repulsions.

Mixed 5f configuration in americium trichloride: Dynamical mean‐field theory combined with density functional theory study

AbstractThe electronic properties in particular the occupation number of 5f electrons and the valence state of Am ions in americium trichloride (AmCl3) are studied by using density functional theory (DFT) merged with dynamical mean‐field theory (DMFT). We find that j = 5/2, j = 7/2 manifolds both are in the insulating regimes, resulting in the semiconducting band gap of about 0.837 eV, together with the weak Am 5f‐conduction electrons hybridization and the localized 5f‐derived spectra feature in the vicinity of the Fermi level. The weighted summation for the occupation probabilities of 5fn (n = 3–7) atomic configurations suggests that 5f electrons have the inter‐configuration fluctuation with an average occupation number of 5f electrons n5f ~ 5.182, corresponding to the valence state of Am3.818+ in AmCl3. The 5fn‐mixing‐driven inter‐configuration fluctuation might originate from the complicated quantum mechanics processes such as the dual nature of 5f electrons and the flexible electronic configuration of Am ions. Finally, the so‐called quasiparticle band structure is also predicted.

Simple lattice model explains equilibrium separation phenomena in glassy polymers.

The Robeson bound is a theoretical limit that applies to kinetics-driven membrane separations of gas mixtures. However, this bound does not apply to sorption-driven membrane processes such as CO2/N2 separation, which lacks a theoretical explanation. As a result, we are uncertain about the factors that control the limiting behavior of sorption-driven separations. To address this issue, we employed a simple lattice model and dynamic mean field theory to examine the transport properties of disordered model structures, isolating sorption effects from purely kinetic effects. Our findings indicate that transport effects play a crucial role in sorption-driven processes, and perm-selectivity is consistently lower than sorption selectivity, which is an unattainable limit. We used basic geometric fragments of the structure to explain how transport effects emerge and manifest themselves in sorption-driven processes.

Valence Fluctuation of Uranium Ions in Uranium Sesquinitride Revealed by Dynamical Mean-field Theory Merged with Density Functional Theory.

The electronic properties, in particular, the occupation number of 5f electrons and the valence state of U ions in uranium sesquinitride (U2 N3 ) are studied by using density functional theory (DFT) calculations merged with dynamical mean-field theory (DMFT). The results demonstrate that j=5/2 and j=7/2 manifolds are in the weakly correlated metallic and weakly correlated insulating regimes, respectively. The quasi-particle weights indicate that LS coupling scheme is more feasible for 5f electrons, which are not in the orbital-selective localized state. The weighted summation of the occupation probabilities of 5fn (n=0,1,2,3,4) atomic configurations suggests that 5f electrons have the inter-configuration fluctuation, or the mixed-valence state for U ions, together with an average occupation number of 5f electrons n5f ∼2.234, which is in good agreement with the electron localization function (ELF) and occupation analysis based on other DFT-based calculations. The 5fn -mixing-driven inter-configuration fluctuation might originate from the dual nature of 5f electrons, and the flexible electronic configuration of U ions. Finally, the so-called quasiparticle band structure is also discussed.

Multiorbital Nature of Doped Sr_{2}IrO_{4}.

The low-energy j_{eff}=1/2 band of Sr_{2}IrO_{4} bears stark resemblances with the x^{2}-y^{2} band of La_{2}CuO_{4}, and yet no superconductivity has been found so far by doping Sr_{2}IrO_{4}. Behind such a behavior could be inherent failures of the j_{eff}=1/2 picture, in particular when electrons or holes are introduced in the IrO_{2} planes. In view of this, here we reanalyze the j_{eff}=1/2 scenario. By using the local-density approximation plus dynamical mean-field theory approach, we show that the form of the effective j_{eff}=1/2 state is surprisingly stable upon doping. This supports the j_{eff}=1/2 picture. We show that, nevertheless, Sr_{2}IrO_{4} remains in essence a multiorbital system: The hybridization with the j_{eff}=3/2 orbitals sizably reduces the Mott gap by enhancing orbital degeneracy, and part of the holes go into the j_{eff}=3/2 channels. These effects cannot be reproduced by a simple effective screened Coulomb repulsion. In the optical conductivity spectra, multiorbital processes involving the j_{eff}=3/2 states contribute both to the Drude peak and to relatively low-energy features.

Synthesis of Single Crystals of ε-Iron and Direct Measurements of Its Elastic Constants.

Seismology finds that Earth's solid inner core behaves anisotropically. Interpretation of this requires a knowledge of crystalline elastic anisotropy of its constituents-the major phase being most likely ε-Fe, stable only under high pressure. Here, single crystals of this phase are synthesized, and its full elasticity tensor is measured between 15 and 33GPa at 300K. It is calculated under the same conditions, using the combination of density functional theory and dynamical mean field theory, which describes explicitly electronic correlation effects. The predictive power of this scheme is checked by comparison with measurements; it is then used to evaluate the crystalline anisotropy in ε-Fe under higher density. This anisotropy remains of the same amplitude up to densities typical of Earth's inner core.

Structure-driven electron transition in cerium mononitride: Insights from density functional theory combined with dynamical mean-field theory

A first principle calculation is implemented with the NaCl-type and CsCl-type structures, respectively, to reveal the structure-driven 4f electron transition in cerium monoarsenide (CeN). It is found that, for the NaCl-type structure, with increasing the lattice constants, the j=5/2 manifold undergoes the insulating→metallic transition, while the j=7/2 state maintains the insulating regime. Quasi-particle weights indicate that the electronic properties of the j=5/2 manifold are significantly renormalized by the crystal structure and/or lattice constant. 4f1 atomic configuration dominates the average occupation numbers of 4f electrons for both NaCl-type and CsCl-type structures. The structure-occupation diagram suggests that the electronic properties of 4f electrons could be modulated in terms of the crystal structure (or phase transition) and/or lattice constant (or pressure).

Condensation phases in a non-Hermitian optical lattices system

We explore the condensate phase of single-species bosons in an optical lattice through the use of dissipative Bose–Hubbard models. The ground state of system possesses a real-energy, which corresponds to non-Hermitian Hamiltonians with non-reciprocal hopping phase factors. Through the application of inhomogeneous dynamical Gutzwiller mean-field theory (DGMFT), we predict a fascinating phenomenon: the ground state displays a periodic arrangement of superfluid islands amidst a Mott insulator sea. Additionally, the number of superfluid islands is proportional to the spatial period squared.

Dynamical mean field theory extension to the nonequilibrium two-particle self-consistent approach

Dynamical mean field theory extension to the nonequilibrium two-particle self-consistent approach

Role of electron correlation and disorder on the electronic structure of layered nickelate (La0.5Sr0.5)2NiO4

We investigate the role of electron correlation and disorder on the electronic structure of layered nickelate ${({\mathrm{La}}_{0.5}{\mathrm{Sr}}_{0.5})}_{2}{\mathrm{NiO}}_{4}$ using core level and valence band photoemission spectroscopy in conjunction with density functional theory (DFT) and dynamical mean-field theory (DMFT) calculations. Sr $3d$ and La $4d$ core level spectra exhibit multiple features associated with photoemission final-state effects. An increase of unscreened features in the Sr $3d$ and La $4d$ core level spectra with lowering temperature suggests the reduction in density of states (DOS) at the Fermi level, ${E}_{F}$. Valence band spectra collected using different photon energies reveal finite intensity at ${E}_{F}$ and overall spectra are well captured by $\mathrm{DFT}+\mathrm{DMFT}$. Strong renormalization of partially filled ${e}_{g}$ bands in $\mathrm{DFT}+\mathrm{DMFT}$ result indicates strong correlation in this system. Mass enhancement factor, ${m}^{*}/{m}_{\text{DFT}}\ensuremath{\sim}$ 3, agrees well with values obtained from specific heat measurements. High-resolution spectra in the vicinity of ${E}_{F}$ show monotonically decreasing spectral intensity with lowering temperature, which evolves to exhibit a Fermi cutoff at low temperatures indicating metallic character in contrast to insulating transport, suggesting Anderson insulating state. $|E\ensuremath{-}{E}_{F}{|}^{1/2}$ dependence of the spectral DOS and square-root temperature dependence of spectral DOS at ${E}_{F}$ evidences the role of disorder in the electronic structure of ${({\mathrm{La}}_{0.5}{\mathrm{Sr}}_{0.5})}_{2}{\mathrm{NiO}}_{4}$.

Tetragonal Kondo Insulator EuCd2Sb2 Discovered via High Pressure High Temperature Synthesis

AbstractMagnetic and electronic properties of quantum materials heavily rely on the crystal structure even in the same chemical compositions. In this study, it is demonstrated that a layered tetragonal EuCd2Sb2 structure can be obtained by treating bulk trigonal EuCd2Sb2 under high pressure (6 GPa) and high temperature (600 °C). Magnetization measurements of the newly formed layered tetragonal EuCd2Sb2 confirm an antiferromagnetic ordering with Neel temperature (TN) around 16 K, which is significantly higher than that (TN ≈ 7 K) of trigonal EuCd2Sb2, consistent with heat capacity measurements. Moreover, bad metal behavior is observed in the temperature dependence of the electrical resistivity and the resistivity shows a dramatic increase around the Neel temperature. Electronic structure calculations with local density approximation dynamic mean–field theory (LDA+DMFT) show that this material is strongly correlated with well‐formed large magnetic moments, due to Hund's coupling, which is known to dramatically suppress the Kondo scale.

Electron correlation e ects in paramagnetic cobalt

We study the influence of Coulomb correlations on spectral and magnetic properties of fcc cobalt using a combination of density functional theory and dynamical mean-field theory. The computed uniform and local magnetic susceptibilities obey the Curie–Weiss law, which, as we demonstrate, occurs due to the partial formation of local magnetic moments. We find that the lifetime of these moments in cobalt is significantly less than in bcc iron, suggesting a more itinerant magnetism in cobalt. In contrast to the bcc iron, the obtained electron self-energies exhibit a quasiparticle shape with the quasiparticle mass enhancement factor m*/m ~ 1.8, corresponding to moderately correlated metal. Finally, our calculations reveal that the static magnetic susceptibility of cobalt is dominated by ferromagnetic correlations, as evidenced by its momentum dependence.

Low-rank Green's function representations applied to dynamical mean-field theory

Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well as efficient interpolation grids used to recover the representations. In particular, the intermediate representation with sparse sampling and the discrete Lehmann representation (DLR) make use of low rank compression techniques to obtain optimal approximations with controllable accuracy. We consider the use of the DLR in dynamical mean-field theory (DMFT) calculations, and in particular show that the standard full Matsubara frequency grid can be replaced by the compact grid of DLR Matsubara frequency nodes. We test the performance of the method for a DMFT calculation of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ at temperature $50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ using a continuous-time quantum Monte Carlo impurity solver, and demonstrate that Matsubara frequency quantities can be represented on a grid of only 36 nodes with no reduction in accuracy, or increase in the number of self-consistent iterations, despite the presence of significant Monte Carlo noise.

Exchange interactions in iron and nickel: DFT+DMFT study in paramagnetic phase

We analyze possible ways to calculate magnetic exchange interactions within the density functional theory plus dynamical mean-field theory (DFT+DMFT) approach in the paramagnetic phase. Using the susceptibilities obtained within the ladder DMFT approach together with the random phase approximation result for the Heisenberg model, we obtain bilinear exchange interactions. We show that the earlier obtained result of Stepanov et al. [Phys. Rev. Lett. 121, 037204 (2018); Phys. Rev. B 105, 155151 (2022)] corresponds to considering individual magnetic moments in each orbital in the leading-order approximation in the non-local correlations. We consider a more general approach and apply it to evaluate the effective magnetic parameters of iron and nickel. We show that the analysis, based on the inverse orbital-summed susceptibilities, yields reasonable results for both, weak and strong magnets. For iron we find, in the low-temperature limit, the exchange interaction $J_0\simeq 0.20$ eV, while for nickel we obtain $J_0\simeq 1.2$ eV. The considered method also allows one to describe the spin-wave dispersion at temperatures $T\sim T_C$, which is in agreement with the experimental data.

Commensurate and spiral magnetic order in the doped two-dimensional Hubbard model: Dynamical mean-field theory analysis

We develop a dynamical mean-field theory approach for the spiral magnetic order, changing to a local coordinate frame with preferable spin alignment along the $z$-axis, which can be considered with the impurity solvers treating the spin diagonal local Green's function. We furthermore solve the Bethe-Salpeter equations for nonuniform dynamic magnetic susceptibilities in the local coordinate frame. We apply this approach to describe the evolution of magnetic order with doping in the $t-t'$ Hubbard model with $t'=0.15$, which is appropriate for the description of the doped La$_2$CuO$_4$ high-temperature superconductor. We find that with doping the antiferromagnetic order changes to the $(Q,\pi)$ incommensurate one, and then to the paramagnetic phase. The spectral weight at the Fermi level is suppressed near half filling and continuously increases with doping. The dispersion of holes in the antiferromagnetic phase shows qualitative agreement with the results of the $t$-$J$ model consideration. In the incommensurate phase we find two branches of hole dispersions, one of which crosses the Fermi level. The resulting Fermi surface forms hole pockets. We also consider the dispersion of the magnetic excitations, obtained from the non-local dynamic magnetic susceptibilities. The transverse spin excitations are gapless, fulfilling the Goldstone theorem; in contrast to the mean-field approach the obtained magnetic state is found to be stable. The longitudinal excitations are characterized by a small gap, showing the rigidity of the spin excitations. For realistic hopping and interaction parameters we reproduce the experimentally measured spin-wave dispersion of La$_2$CuO$_4$.

Structure of the normal state and origin of the Schottky anomaly in the correlated heavy-fermion superconductor UTe2

The recently discovered $\mathrm{U}{\mathrm{Te}}_{2}$ superconductor is regarded as a heavy-fermion mixed-valence system with very peculiar properties within the normal and superconducting (SC) states. It shows no signs of magnetic order, but has a strong anisotropy of magnetic susceptibility and SC critical field. In addition to a heavy-fermion-like behavior in the normal state, it exhibits a distinctive Schottky-type anomaly at $\ensuremath{\sim}12$ K and a characteristic excitations gap $\ensuremath{\sim}35\ensuremath{-}40$ K. Here, we show, by virtue of dynamical mean-field theory calculations with a quasiatomic treatment of electron correlations, that ab initio-derived crystal-field splitting of the $5{f}^{2}$ ionic configuration yields agreement with these experimental observations. A close analogy of the normal paramagnetic state of $\mathrm{U}{\mathrm{Te}}_{2}$ to that of $\mathrm{U}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$ in the Kondo arrest scenario is revealed. We consider the impact of anisotropic superexchange interactions within the U-U structural dimer on magnetization and development of strong orbital and magnetic moment fluctuations in $\mathrm{U}{\mathrm{Te}}_{2}$.

Improved effective vertices in the multiorbital two-particle self-consistent method from dynamical mean-field theory

In this paper, we present a multiorbital form of the two-particle self-consistent approach (TPSC) where the effective local and static irreducible interaction vertices are determined by means of the dynamical mean-field theory (DMFT). This approach replaces the approximate ansatz equations for the double-occupations $\ensuremath{\langle}{n}_{\ensuremath{\alpha},\ensuremath{\sigma}}^{}{n}_{\ensuremath{\beta},{\ensuremath{\sigma}}^{\ensuremath{'}}}^{}\ensuremath{\rangle}$ by sampling them directly for the same model using DMFT. Compared to the usual Hartree-Fock-like ansatz, this leads to more accurate local vertices in the weakly correlated regime and provides access to stronger correlated systems that were previously out of reach. This approach is extended by replacing the local component of the TPSC self-energy by the DMFT impurity self-energy, which results in an improved self-energy that incorporates strong local correlations but retains a nontrivial momentum dependence. We find that this combination of TPSC and DMFT provides a significant improvement over the multiorbital formulation of TPSC as it allows to determine the components of the spin vertex without artificial symmetry assumptions and opens the possibility to include the transversal particle-hole channel. The new approach is also able to remove unphysical divergences in the charge vertices in TPSC. We find a general trend that lower temperatures can be accessed in the calculation. Benchmarking single-particle quantities, such as the local spectral function with other many-body methods, we find significant improvement in the more strongly correlated regime.

Coulomb correlations in a germanide iron-based superconductor: The example of YFe2Ge2

We report results of a detailed theoretical study of the effect of Coulomb correlations on the structural, electronic, and magnetic properties of the non-pnictide iron-based superconductor ${\mathrm{YFe}}_{2}{\mathrm{Ge}}_{2}$. In particular, by employing the density functional theory plus dynamical mean-field theory method ($\mathrm{DFT}+\mathrm{DMFT}$) we perform a structural optimization of the unit-cell volume and the internal coordinate ${z}_{\mathrm{Ge}}$ of Ge. Our results for the lattice parameters obtained by $\mathrm{DFT}+\mathrm{DMFT}$ show a much better agreement with experiment as compared to those calculated by DFT implying the importance of correlation effects. We show that ${\mathrm{YFe}}_{2}{\mathrm{Ge}}_{2}$ is a moderately correlated system with electron-electron correlations being strong enough to renormalize the low-energy band structure but not sufficient to form Hubbard bands, in close analogy to the iron-based pnictides and chalcogenides. The analysis of the local spin-spin correlation function and momentum-dependent spin susceptibility $\ensuremath{\chi}(\mathbf{q})$ indicates the correlation induced formation of short-lived local moments in the Fe ${t}_{2g}$ states and the presence of competing spin fluctuations, in agreement with experiment.