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Computation 2016, 4(3), 34; doi:10.3390/computation4030034

Towards TDDFT for Strongly Correlated Materials

Department of Physics, University of Central Florida, Orlando, FL 32816, USA
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Author to whom correspondence should be addressed.
Academic Editor: Karlheinz Schwarz
Received: 31 May 2016 / Revised: 23 August 2016 / Accepted: 1 September 2016 / Published: 10 September 2016
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Abstract

We present some details of our recently-proposed Time-Dependent Density-Functional Theory (TDDFT) for strongly-correlated materials in which the exchange-correlation (XC) kernel is derived from the charge susceptibility obtained using Dynamical Mean-Field Theory (the TDDFT + DMFT approach). We proceed with deriving the expression for the XC kernel for the one-band Hubbard model by solving DMFT equations via two approaches, the Hirsch–Fye Quantum Monte Carlo (HF-QMC) and an approximate low-cost perturbation theory approach, and demonstrate that the latter gives results that are comparable to the exact HF-QMC solution. Furthermore, through a variety of applications, we propose a simple analytical formula for the XC kernel. Additionally, we use the exact and approximate kernels to examine the nonhomogeneous ultrafast response of two systems: a one-band Hubbard model and a Mott insulator YTiO3. We show that the frequency dependence of the kernel, i.e., memory effects, is important for dynamics at the femtosecond timescale. We also conclude that strong correlations lead to the presence of beats in the time-dependent electric conductivity in YTiO3, a feature that could be tested experimentally and that could help validate the few approximations used in our formulation. We conclude by proposing an algorithm for the generalization of the theory to non-linear response. View Full-Text
Keywords: density functional theory; time-dependent phenomena; strongly-correlated materials; dynamical mean field theory; ultrafast response density functional theory; time-dependent phenomena; strongly-correlated materials; dynamical mean field theory; ultrafast response
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MDPI and ACS Style

Acharya, S.R.; Turkowski, V.; Rahman, T.S. Towards TDDFT for Strongly Correlated Materials. Computation 2016, 4, 34.

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