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Generalized density functional theory framework for the nonlinear density response of quantum many-body systems

Zhandos A. Moldabekov1,*, Cheng Ma2,3, Xuecheng Shao2,3,4, Sebastian Schwalbe1, Pontus Svensson1, Panagiotis Tolias5, Jan Vorberger1, and Tobias Dornheim1,6

  • *Contact author: z.moldabekov@hzdr.de
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Phys. Rev. B 113, 125115 – Published 9 March, 2026

DOI: https://doi.org/10.1103/56xx-12ts

Abstract

A density functional theory (DFT) framework is presented that links functional derivatives of free-energy functionals to nonlinear static density response functions in quantum many-body systems. Within this framework, explicit expressions are derived for various higher-order response functions of systems that are homogeneous on average, including the first theoretical result for the cubic response at the first harmonic χ0(1,3)(q). Specifically, our framework includes hitherto neglected mode-coupling effects that are important for the nonlinear density response even in the presence of a single harmonic perturbation. We compare these predictions for χ0(1,3)(q) to new Kohn-Sham DFT simulations, leading to excellent agreement between theory and numerical results. Exact analytical expressions are also obtained for the long-wavelength limits of the ideal quadratic and cubic response functions. Particular emphasis is placed on the connections between the third- and fourth-order functional derivatives of the noninteracting free-energy functional Fs[n] and the ideal quadratic and cubic response functions of the uniform electron gas, respectively. These relations provide exact constraints that may prove useful for the future construction of improved approximations to Fs[n], in particular, for warm dense matter applications at finite temperatures. Here, we use this framework to assess several commonly employed approximations to Fs[n] through orbital-free DFT simulations of the harmonically perturbed ideal electron gas. The results are compared with Kohn-Sham DFT calculations across temperatures ranging from the ground state to the warm dense regime. Additionally, we analyze in detail the temperature- and wave number-dependent nonmonotonic behavior of the ideal quadratic and cubic response functions.

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Phys. Rev. B 113, 125115– Published 9 March, 2026
  • Received 8 December 2025
  • Revised 3 February 2026
  • Accepted 19 February 2026
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