Fractionalization is among the most intriguing phenomena in quantum many-body systems, reminiscent of the deconfinement of quarks in the early universe. It showcases a non-trivial consequence of many-body entanglement, which seemingly violates quantization, a fundamental aspect of quantum mechanics. Furthermore, fractionalization has offered a new avenue for exploring various interesting physics, such as high temperature superconductivity and topological quantum computation. However, despite extensive efforts over the past several decades, a clear experimental demonstration of fractionalization outside of fractional quantum Hall insulators has remained elusive.
In this talk, I will present my journey on searching for fractionalization in exotic quantum critical systems. Starting from how microscopic information can constrain the possible quantum phases, I will examine three promising experimental platforms for exotic criticalities: Moire materials, layered oxides, and Rydberg quantum simulators. In these systems, different quantum orders compete, resulting in the conventional degrees of freedom becoming inadequate to describe the system and inducing fractionalization. Numerical simulations using iDMRG will be presented alongside theoretical analysis of the emergent critical properties. Finally, experimental signatures for fractionalization will be discussed, highlighting the opportunities provided by recent advancements in "designer" materials.