Wannier-function software ecosystem for materials simulations

Over the past two decades, following the early developments on maximally localized Wannier functions, an ecosystem of electronic-structure simulation techniques and software packages leveraging the Wannier representation has flourished. This environment includes codes to obtain Wannier functions and interfaces with first-principles simulation software, as well as an increasing number of related postprocessing packages. Wannier functions can be obtained for isolated or extended systems (both crystalline and disordered) and can be used to understand chemical bonding; to characterize electric polarization, magnetization, and topology; and as an optimal basis set, providing accurate interpolations in reciprocal space or large-scale Hamiltonians in real space. This review summarizes the current landscape of techniques, materials properties, and simulation codes based on Wannier functions that have been made accessible to the research community and that are now well integrated into what is referred to as a Wannier-function software ecosystem. To begin, the theory and practicalities of Wannier functions, starting with their broad domains of applicability to advanced minimization methods using alternative approaches beyond maximal localization, are introduced. The concept of a Wannier ecosystem and its interactions and interoperability with many quantum simulations engines and postprocessing packages are then defined. The review focuses on some of the key properties and capabilities that are empowered by such an ecosystem (from band interpolations and large-scale simulations to electronic transport, Berryology, topology, electron-phonon couplings, dynamical mean-field theory, embedding, and Koopmans functionals) and concludes with the current status of interoperability and automation. The review aims at highlighting the basic theory and concepts behind codes while providing mentions of more in-depth references. It also elucidates the relationships and connections between codes and, where relevant, the different motivations and objectives behind their development strategies. Finally, an outlook on future developments is provided and comments are made on the goals of biodiversity and sustainability for the entire software ecosystem.