Numerical methods provide an indispensable toolbox for unravelling equilibrium and out-of-equilibrium properties of quantum materials, where the interplay of topology, disorder and interactions is paramount. Specialised algorithms with non-exponential complexity have helped predict and understand a rich array of phenomena, including the electronic structure and optical response of strongly correlated systems, exotic ordering in quantum magnets, spin transport in nanostructures and unconventional superconductivity. Boosted by efficient computer implementations, the numerical simulation of quantum matter has reached unprecedented milestones in accuracy, versatility, and achievable system sizes.

This mini-colloquium aims to bring together the research community interested in the development and applications of real-space simulation approaches, including, but not limited to, density matrix renormalization group algorithms, dynamical mean-field theory, spectral expansions and non-equilibrium Green’s function-based techniques. A grand challenge focus on van der Waals materials with large unit cells (e.g. twisted bilayer graphene) will contribute to the mini-colloquium aim of expanding the open-science community engagement in the development of accurate tools for understanding exotic low-temperature phases of two-dimensional materials and related heterostructures.

The event will build upon the online CMD workshop organized in Oct 2021 and will provide an interactive venue to share recent developments in real-space methodologies, efficient numerical methods, and their implementation, identify open problems and envision future research directions.

Contributions covering the following topics are encouraged:

• Emerging trends in numerical simulation of condensed phases of matter
• Non-equilibrium dynamics of many-body systems
• Disorder effects in electronic and quantum transport properties
• Electronic structure of topological / strongly correlated materials
• Coupled charge-spin transport in nanostructures

We acknowledge the generous sponsorship provided by The Royal Society [grant No. URF\R\191021 (AF)].