Dirac fermions with plaquette interactions. II. SU(4) phase diagram with Gross-Neveu criticality and quantum spin liquid

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 moire mate-rials, 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.

Automated summary

This study utilizes large-scale quantum Monte Carlo simulations to investigate correlated electron systems and discovers the presence of a Gross-Neveu quantum critical point and a Dirac quantum spin liquid. These findings have significant implications for quantum many-body theory and the understanding of experimental systems.