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

TL;DR

This paper uses large-scale quantum Monte Carlo simulations to reveal a rich phase diagram in a 2D lattice model, featuring a Gross-Neveu quantum critical point, a Dirac quantum spin liquid, and emergent phenomena relevant to quantum many-body systems.

Contribution

It uncovers a sequence of novel quantum states, including a Gross-Neveu critical point and a Dirac quantum spin liquid, in a simple lattice model with extended Hubbard interactions.

Findings

Identification of a Gross-Neveu quantum critical point separating Dirac fermions and valence bond solid.

Evidence for a possible Dirac quantum spin liquid at strong coupling.

Emergence of symmetry, fractionalization, and matter-gauge field coupling in the model.

Abstract

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, ultra-cold atoms, frustrated magnets and quantum Moir\'e materials, their unbiased presence remain 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 extended Hubbard interaction, that a Gross-Neveu QCP separating massless Dirac fermions and an 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 novel quantum states resides in this simple-looking model, unifying ingredients including emergent symmetry, deconfined fractionalization and the dynamic coupling between emergent matter and gauge fields, will have profound implications both in quantum many-body theory and understanding of the aforementioned experimental systems.