Universal behavior beyond multifractality in quantum many-body systems.

How many states of a configuration space contribute to a wave function? Attempts to answer this ubiquitous question have a long history in physics and are keys to understanding, e.g., localization phenomena. Beyond single-particle physics, a quantitative study of the ground state complexity for interacting many-body quantum systems is notoriously difficult, mainly due to the exponential growth of the configuration (Hilbert) space with the number of particles. Here we develop quantum Monte Carlo schemes to overcome this issue, focusing on Shannon-Rényi entropies of ground states of large quantum many-body systems. Our simulations reveal a generic multifractal behavior while the very nature of quantum phases of matter and associated transitions is captured by universal subleading terms in these entropies.