Advancing the theory of quantum phase transitions in the era of quantum computing

Understanding quantum phase transitions is one of the biggest challenges in modern physics, stimulating numerous exciting developments in theoretical, experimental, and numerical physics. Perhaps, the most remarkable, was the invention of conformal field theory, responsible for many exact predictions. This paved the way for numerical and experimental observations of many of these transitions forming, however, a misleading impression that almost all quantum transitions in nature are conformal. But is this imbalance real, or are many exciting non-conformal transitions currently overlooked due to the limitations of our theoretical toolbox?In this proposal, I aim to develop a methodology for the unbiased construction of quantum phase transitions. Recent years have been marked by tremendous progress in non-perturbative computational methods. The invention of constrained tensor networks fully profiting from Rydberg blockade for the first time provides sufficient accuracy to predict novel types of quantum phase transitions. With such a powerful tool at hand, I aim to develop a numerical approach to engineer novel quantum criticalities in experimentally realizable models of Rydberg atoms. Implemented directly on a lattice, my method will not rely on the available field-theoretic description of the transitions and, by construction, will have no bias towards conformal ones, opening a way for systematic study of non-conformal transitions and breaking a new ground in fundamental physics. By focusing directly on the effective models of Rydberg atoms I open a path for immediate experimental validation of my future predictions. This proposal benefits from the latest technological advances and will provide a timely theory guidance for future experiments. My study will be an important step towards synthesising novel quantum critical phenomena directly in quantum simulators.