At sufficiently low temperatures, interacting electron systems tend to develop orders. Exceptions are quantum critical point (QCP) and quantum spin liquid (QSL), where fluctuations prevent the highly entangled quantum matter to an ordered state down to the lowest temperature. While the ramification of these states may have appeared in high-temperature superconductors, ultracold atoms, frustrated magnets, and quantum moiré materials, their unbiased presence remains elusive in microscopic two-dimensional lattice models. Here, we show, by means of large-scale quantum Monte Carlo simulations of correlated electrons on the $\pi$-flux square lattice subjected to plaquette Hubbard interaction, that a Gross-Neveu QCP separating massless Dirac fermions and a columnar valence bond solid at finite interaction and a possible Dirac QSL at the infinite yet tractable interaction limit emerge in a coherent sequence. These unexpected quantum states reside in this simple-looking model, unifying ingredients including emergent symmetry, deconfined fractionalization, and the dynamic coupling between emergent matter and gauge fields and will have profound implications both in quantum many-body theory and understanding of the aforementioned experimental systems.

• Received 18 July 2022
• Revised 18 September 2022
• Accepted 19 September 2022

DOI:https://doi.org/10.1103/PhysRevB.106.115149