Strong correlation physics in Moiré, Nickelate and Kagome superconductors

The interplay between strong electronic correlations and the laws of quantum physics can lead to exotic new states of matter. Turning novel materials into future technologies requires a thorough theoretical understanding of the fundamental physical phenomena encountered. Advances in computational methods in recent years allow for the study of strongly interacting quantum many-body systems with unprecedented accuracy, enabling us to explore questions posed by recent material discoveries.Kagome metals exhibit superconductivity, unconventional charge density waves, and possible time-reversal symmetry breaking, whose origin remains unknown. Nickelate superconductors are a structural analog of cuprate superconductors. However, they exhibit several crucial differences likely due to genuine multi-orbital physics whose treatment has so far been considered theoretically challenging. Moiré transition metal dichalcogenides stabilize various Mott insulating states with the possibility of hosting an elusive chiral spin liquid state, for which the understanding of crucial thermal and dynamical signatures is still missing. MoNiKa aims to reveal their fundamental physical properties by studying microscopic models capturing the essential physical aspects of these materials. These models include the extended kagome lattice Hubbard models for the kagome metals, multi-orbital Hubbard-Kanamori models for the nickelate superconductors, and dynamical properties of triangular lattice Hubbard models for the moiré transition metal dichalcogenides.To tackle these problems, we will utilize a comprehensive set of advanced numerical techniques, emphasizing novel finite temperature tensor network methods. While simultaneously extending the boundaries of these computational approaches, we will characterize superconductivity, new forms of magnetism, Mott insulators, and charge density waves alongside their thermal and dynamical signatures.