Transforming the Computational Workhorse of Electronic Structure
Density-functional theory (DFT) has long been the best tool for describing the equilibrium ground states of many-body systems, such as a material’s electronic structure. But its time-dependent counterpart (TDDFT)—one of the most viable computational methods for treating nonequilibrium versions of similar systems—is less effective. Now Éric Cancès at the Paris Polytechnic Institute and his colleagues have developed a new formulation of TDDFT based on geometric concepts [1].
Standard TDDFT is based on a theorem that states that the complex dynamics of an out-of-equilibrium quantum many-body system can be approximated by applying a single external potential and adjusting it over time. But to capture the behaviors of many interacting particles, this potential-energy landscape often develops sharp peaks and steps, which are difficult to model numerically. Cancès and his colleagues showed that this problem can be avoided by reformulating the system’s evolution geometrically. Instead of imposing a jagged, hard-to-model, real-energy landscape, they used an imaginary (complex) potential. In this approach, the system’s path is constrained to a surface within a multidimensional space of valid particle configurations, which ensures that the governing potentials remain smooth and continuous.
The researchers tested their approach by applying it to systems of noninteracting particles and predicting how the systems would evolve if the particles were fully interacting. Using exactly solvable 1D numerical simulations as benchmarks, they compared these predictions to those obtained using conventional TDDFT. They found that the new geometric TDDFT captured abrupt shocks to a system’s equilibrium more accurately. They say that this ability to describe such violent perturbations could be especially useful for modeling charge transfer in complex molecules, ultrafast phenomena, and other strongly driven out-of-equilibrium systems.
–Rachel Berkowitz
Rachel Berkowitz is a Corresponding Editor for Physics Magazine based in Vancouver, Canada.
References
- É. Cancès et al., “Geometric time-dependent density functional theory,” Phys. Rev. Lett. 136, 256401 (2026).