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Ferdi Aryasetiawan

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Research

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aryasetiawan - Google Scholar

My current research activities are focused on developing a new route for calculating the Green function of many-electron systems. The Green function is an indispensable quantity in condensed-matter physics since a wide range of fundamental physical properties, notably those related to one-particle excitations measured in photoemission and inverse photoemission, can be derived from it. For example, Fermi surface, quasiparticle dispersion, and density of states or spectral function are among those.

Since its conception in the 1950's, the Green function has been synonymous with the self-energy. The self-energy is traditionally calculated using many-body perturbation theory, such as the well-established Hedin GW approximation (Hedin 1965, 1969) and the fluctuation-exchange (FLEX) approximation (Bickers 1989), in which Feynman diagrams are summed to infinite order. For systems with strong correlations, non-perturbative approach, such as dynamical mean-field theory (DMFT) (Georges 1996), is usually mandatory. A common denominator of these approaches is high computational cost to the point that applications to complex materials with many atoms in a unit cell is not feasible. Expensive and complicated calculations must be performed for each and every material.

This situation is in strong contrast to calculations of ground-state properties, in which Kohn-Sham density functional theory (DFT) (Hohenberg 1964, Kohn 1965, 1999, Jones 1989, 2015, Becke 2014) has made applications to complex materials feasible. The DFT approach is based on a universal functional for the exchange-correlation energy and applicable to all electronic systems. The exchange-correlation energy of the interacting homogeneous electron gas is calculated once and for all using an accurate quantum Monte Carlo method (Ceperley 1980) and applied to real materials within the local-density approximation and its improvements. Thus, expensive and complicated ground-state energy calculations of real materials, using, e.g., quantum Monte Carlo method, are circumvented. It would be at present unrealistic to use the quantum Monte Carlo method to calculate the ground-state energy of real materials, with exception of some simple systems, perhaps.

A theory corresponding to density-functional theory for calculating the excitation spectra is absent at present. Recently, a different route for calculating the Green function based on the concept of correlation between the ground-state electron density and the Green function was discovered (Aryasetiawan 2022a). It is shown that the Green function follows an equation of motion under a time-dependent exchange-correlation field that acts locally, and most importantly, this exchange-correlation field arises as the Coulomb potential of a dynamic exchange-correlation hole that fulfils a sum rule, namely, it integrates to -1 for hole (negative time) and 0 for electron (positive time).  The static limit of this dynamic exchange-correlation hole reduces to the well-known static exchange-correlation hole. Hence, a close link to electron density and density-functional theory is established and it is envisaged that a simple approximation along the line of the local-density approximation may be fruitful. Results for the one-dimensional Hubbard chain (Aryasetiawan 2022b) and the electron gas (Karlsson 2023) indicate the “near-sightedness” (Kohn 1996, Prodan 2005) of the exchange-correlation field, suggesting that an approximation based on local quantities such as the local-density-like approximation may work well.

My previous research activities have been compiled in a recent book publication (Aryasetiawan 2022c). They have been centred around development of theoretical methods for calculating from first-principles the electronic structure of real materials, in particular those in which electron correlations are strong. These strongly correlated materials are abundant in nature and yet accurate description of their electronic structure is elusive. These materials are characterised by the presence of 3d or 4f elements such as transition metal atoms (3d) or lanthanides (4f), whose orbitals form partially filled bands. Famous examples of these materials are the cuprates high-temperature superconductors, materials possessing colossal magneto resistance, and magnetic materials in general.

The commonly used method for computing the electronic structure is density functional theory within the local density approximation (LDA) and its variants. However, for strongly correlated materials, this conventional method has been found to fail in many cases. For example, insulators are often predicted to be metals. A successful method beyond the LDA based on the Green's function technique is the GW approximation (Aryasetiawan 1998), which has been shown to be highly accurate to describe the electronic structure of metals and semiconductors in which the valence states originate from s or p electrons. Thus, the well-known underestimation of band gaps in semiconductors is very much removed within the GW approximation. However, for strongly correlated systems, even the GW approximation is not sufficient. For these systems, a suitable method is dynamical mean-field theory (DMFT) (Georges 1996), which maps the lattice problem to an Anderson impurity problem.

DMFT has a number of shortcomings, such as the assumption of local self-energy as well as a problem of double-counting when combined with LDA. In collaboration with Antoine Georges and Silke Biermann, a combination of the GW approximation and DMFT, dubbed GW+DMFT, was developed (Biermann 2003). This GW+DMFT method overcomes the shortcomings of DMFT while at the same time takes advantage of the GW approximation, making the method free from adjustable parameters. The method has been successfully applied to a number of systems resulting in new interpretation of the spectral function (density of states) in the materials studied [Boehnke 2016, Nilsson 2017]. It has also been applied to more complex materials such as the d(1,2,3) perovskites (Petocchi 2020a) and later to the recently discovered nicklate superconductor Nd1-xSrxNiO2, in which new insights into its normal state not realised before have been obtained (Petocchi 2020b).

References

Aryasetiawan, F. 2022a, Time-dependent exchange-correlation potential in lieu of self-energy, Phys. Rev. B 105, 075106.

Aryasetiawan, F. and T. Sjöstrand, 2022b, Spectral functions of the half-filled one-dimensional Hubbard chain within the exchange-correlation potential formalism, Phys. Rev. B 106, 045123.

Aryasetiawan, F. and F. Nilsson, 2002c, Downfolding Methods in Many-Electron Theory, (AIP Publishing, Melville, NY) https://doi.org/10.1063/9780735422490

Becke, A. D., 2014, Perspective: Fifty years of density-functional theory in chemical physics, J. Chem. Phys. 140, 18A301.

Bickers, N. E., D. J. Scalapino, and S. R. White, 1989, Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard} Model, Phys. Rev. Lett. 62, 961.

Biermann, S., F. Aryasetiawan, and A. Georges, 2003, First-Principles Approach to the Electronic Structure of Strongly Correlated Systems: Combining the GW Approximation and Dynamical Mean-Field Theory, Phys. Rev. Lett. 90, 086402.

Boehnke, L., F. Nilsson, F. Aryasetiawan, and P. Werner, 2016, When strong correlations become weak: Consistent merging of GW and DMFT, Phys. Rev. B 94, 201106(R).

Ceperley, D. M. and B. J. Alder, 1980, Ground state of the electron gas by a stochastic method, Phys. Rev. Lett. 45, 566.

Georges, A., G. Kotliar, W. Krauth, and M. J. Rozenberg, 1996, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys. 68, 13.

Hedin, L., 1965, New Method for Calculating the One-Particle {Green's} Function with Application to the Electron-Gas Problem, Phys. Rev. 139, A796.

Hedin, L. and S. Lundqvist, 1969, Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids, Solid State Physics 23 (eds. F. Seits, D. Turnbull and H. Ehrenreich), (Academic Press, NY).

Hohenberg, P. and W. Kohn, 1964, Inhomogeneous electron gas, Phys. Rev. 136, B864.

Jones, R. O. and O. Gunnarsson, 1989, The density functional formalism, its applications and prospects, Rev. Mod. Phys. 61, 689.

Jones, R. O., 2015, Density functional theory: Its origins, rise to prominence, and future, Rev. Mod. Phys. 87, 897.

Kohn, W. and L. J. Sham, 1965, Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. 140, A1133.

Kohn, W., 1996, Density Functional and Density Matrix Method Scaling Linearly with the Number of Atoms, Phys. Rev. Lett. 76, 3168.

Kohn, W., 1999, Nobel Lecture: Electronic structure of matter - wave functions and density functionals, Rev. Mod. Phys. 71, 1253.

Karlsson, K. and F. Aryasetiawan, 2023, Time-dependent exchange-correlation hole and potential of the electron gas, arXiv:2301.05590 (cond-mat.str-el).

Nilsson, F., L. Boehnke, P. Werner, and F. Aryasetiawan, 2017, Multitier self-consistent GW+EDMFT, Phys. Rev. Materials 1, 043803.

Petocchi, F., F. Nilsson, F. Aryasetiawan, and P. Werner, 2020a, Screening from eg states and antiferromagnetic correlations in d(1,2,3) perovskites: A GW+EDMFT investigation, Phys. Rev. Res. 2, 013191.

Petocchi, F., V. Christiansson, F. Nilsson, F. Aryasetiawan, and P. Werner, 2020b, Normal State of Nd1-xSrxNiO2 from Self-Consistent GW+EDMFT, Phys. Rev. X 10, 041047.

Prodan, E. and W. Kohn, 2005, Nearsightedness of electronic matter, PNAS 102, 11635.

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