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Quadratic band touching (QBT) points are widely observed in 2D and 3Dmaterials, including bilayer graphene and Luttinger semimetals, and attractsignificant attention from theory to experiment. However, even in its simplestform, the 2D checkerboard lattice QBT model, the phase diagram characterized bytemperature and interaction strength still remains unknown beyond theweak-coupling regime. Intense debates persist regarding the existence ofvarious interaction-driven insulating states in this system. To address theseuncertainties, we employ thermal tensor network simulations, specificallyexponential tensor renormalization group and tangent space tensorrenormalization group, along with density matrix renormalization groupcalculations to provide a comprehensive finite-temperature phase diagram forthis model and shed light on previous ambiguities. Notably, our findings revealthe emergence of a robust bond-nematic Dirac semimetal phase with distinctthermodynamic properties that set it part from the nematic insulating state andother symmetry broken states. This previously overlooked feature is found to beubiquitous in interacting QBT systems. We also discuss the implications ofthese results for experimental systems such as bilayer graphene and iridatecompounds.

Ubiquitous nematic Dirac semimetal emerging from interacting quadratic band touching system