Nonadiabatic exchange-correlation kernel for strongly correlated materials

Abstract

ABSTRACT. We formulate a rigorous method for calculating a nonadiabatic (frequencydependent) exchange-correlation (XC) kernel required for correct description of both equilibrium and nonequilibrium properties of strongly correlated systems within Time-Dependent Density Functional Theory (TDDFT). To do so we use the expression for charge susceptibility provided by Dynamical Mean Field Theory (DMFT) for the effective multi-orbital Hubbard Model. We tested our formalism by applying it to the one-band Hubbard model: our nonadiabatic kernel leads to a significant modification of the excitation spectrum, shifting the peak that appears in adiabatic (simplified) solutions and disclosing a new one, in agreement with the DMFT solution. We also used our method to track the nonequilibrium charge-density response of a multi-orbital perovskite Mott insulator, YTiO 3 , to a perturbation by a femtosecond (fs) laser pulse. The results were quite different from those provided by the corresponding adiabatic formalism. These initial investigations indicate that electron-electron correlations and nonadiabatic features can significantly affect the spectrum and nonequilibrium properties of strongly correlated systems. Introduction.--Correct description of the physical, including nonequilibrium, properties of strongly correlated electron systems is one of the most important goals of the condensed matter and material science communities. These systems demonstrate unusual properties with many potential applications both in bulk (high-temperature superconductivity, exotic interplay of magnetism and superconductivity, giant magneto-resistance, etc.) (see, for example Ref.[1]) and in the nanocase (for example, antiferromagnetism in small Fe chains, 2 exotic charge carrier generation in the insulating phase of a VO 2 nanosystem, 3 and anomalous lattice expansion 4,5 and room temperature ferromagnetism 6 in CeO 2 nanostructures). From the perspective of technological applications, nanostructures look even more promising than bulk, since they afford additional channels for tuning a system's properties by varying its size and geometry and by putting it on different substrates. Description of experimentally observed properties as well as prediction of new strongly correlated systems with desired properties requires reliable theoretical and computational tools.

Photo-induced phase-transitions in complex solids

“…Recently, the linear-response TDDFT nonadiabatic XC potential (XC kernel) was calculated with DMFT for spin-independent and spin-dependent cases. 50,107 In these studies, the kernels were derived from the DMFT charge and spin susceptibilities, respectively.…”

“…including the time-dependent current density functional theory (TDCDFT) [103,104], time-dependent deformation functional theory (TDDefFT) [105,106] etc., have been made to include memory effects in the xc-potential. Recently, the linear-response TDDFT nonadiabatic XC potential (XC kernel) was calculated with DMFT for spin-independent and spin-dependent cases [50,107]. In these studies, the kernels were derived from the DMFT charge and spin susceptibilities, respectively.…”

Electron correlations and memory effects in ultrafast electron and hole dynamics in VO2

“…To address these issues, one could apply nonequilibrium DMFT [30,31], except that it is computationally prohibitive, particularly for a system that may be spatially nonhomogeneous and contains more than few (1-2) d-orbitals. A more computationally feasible alternative is our recently developed TDDFT+DMFT that combines ab initio and many-body theory approaches [32]. It takes into account time-resolved electron-electron interaction (memory effects) via the XC potential (kernel) that is derived from the DMFT charge susceptibility for an effective Hubbard model.…”

Towards TDDFT for Strongly Correlated Materials

“…We refer the reader to [45,[54][55][56] for details on the static properties of the system obtained with DFT + DMFT and other approaches. The free-electron spectrum of YTiO 3 was obtained by using a tight-binding model with the parameters given in [54].…”