Ubiquitous nematic Dirac semimetal emerging from interacting quadratic band touching system

TL;DR

This paper uses advanced tensor network simulations to map the finite-temperature phase diagram of a 2D quadratic band touching model, revealing a robust nematic Dirac semimetal phase driven by interactions.

Contribution

It provides the first comprehensive finite-temperature phase diagram of the 2D QBT model, identifying a new interaction-driven nematic Dirac semimetal phase.

Findings

Discovery of a robust bond-nematic Dirac semimetal phase

Identification of thermodynamic properties distinguishing this phase

Ubiquity of this phase in interacting QBT systems

Abstract

Quadratic band touching (QBT) points are widely observed in 2D and 3D materials, including bilayer graphene and Luttinger semimetals, and attract significant attention from theory to experiment. However, even in its simplest form, the 2D checkerboard lattice QBT model, the phase diagram characterized by temperature and interaction strength still remains unknown beyond the weak-coupling regime. Intense debates persist regarding the existence of various interaction-driven insulating states in this system. To address these uncertainties, we employ thermal tensor network simulations, specifically exponential tensor renormalization group and tangent space tensor renormalization group, along with density matrix renormalization group calculations to provide a comprehensive finite-temperature phase diagram for this model and shed light on previous ambiguities. Notably, our findings reveal the emergence of a robust bond-nematic Dirac semimetal phase with distinct thermodynamic properties that set it part from the nematic insulating state and other symmetry broken states. This previously overlooked feature is found to be ubiquitous in interacting QBT systems. We also discuss the implications of these results for experimental systems such as bilayer graphene and iridate compounds.