Dirac fermions with plaquette interactions. I. SU(2) phase diagram with Gross-Neveu and deconfined quantum criticalities

TL;DR

This study uses quantum Monte Carlo simulations to explore a square lattice Hubbard model, revealing an intermediate phase with two quantum critical points exhibiting Gross-Neveu and deconfined quantum criticalities, relevant for fermionic systems.

Contribution

It uncovers an intermediate phase with two distinct quantum critical points and characterizes their critical exponents, advancing understanding of quantum criticality in fermionic lattice models.

Findings

Identification of an intermediate phase with VBS and AF order

Observation of Gross-Neveu and deconfined quantum critical points

Critical exponents satisfy CFT Bootstrap bounds

Abstract

We investigate the ground state phase diagram of an extended Hubbard model with $\pi$-flux hopping term at half-filling on a square lattice, with unbiased large-scale auxiliary-field quantum Monte Carlo simulations. As a function of interaction strength, there emerges an intermediate phase which realizes two interaction-driven quantum critical points, with the first between the Dirac semimetal and an insulating phase of weak valence bond solid (VBS) order, and the second separating the VBS order and an antiferromagnetic insulating phase. These intriguing quantum critical points are respectively bestowed with Gross-Neveu and deconfined quantum criticalities, and the critical exponents $\eta_\text{VBS}=0.6(1)$ and $\eta_\text{AF}=0.58(3)$ at deconfined quantum critical point satisfy the CFT Bootstrap bound. We also investigate the dynamical properties of the spin excitation and find the spin gap open near the first transition and close at the second. The relevance of our findings in realizing deconfined quantum criticality in fermion systems and the implication to lattice models with further extended interactions such as those in quantum Moir\'e systems, are discussed.