Interaction-induced nematic Dirac semimetal from quadratic band touching: A constrained-path quantum Monte Carlo study

TL;DR

This study uses advanced quantum Monte Carlo simulations to reveal an interaction-induced bond-nematic Dirac semimetal phase in a model of spinless fermions on a checkerboard lattice, clarifying the phase diagram.

Contribution

It introduces an improved CP-QMC method to identify a novel bond-nematic Dirac semimetal phase, inaccessible to mean-field approaches, in the phase diagram of the model.

Findings

Identified three phases: quantum anomalous Hall insulator, bond-nematic Dirac semimetal, and site-nematic insulator.

Validated CP-QMC results with DMRG on small lattices, showing quantitative agreement.

Established the emergence of the bond-nematic Dirac semimetal phase in the thermodynamic limit.

Abstract

Electronic systems with quadratic band touchings, commonly found in two- and three-dimensional materials such as Bernal-stacked bilayer graphene, kagome metals, HgTe, and pyrochlore iridates, have attracted significant interest concerning the role of interactions in shaping their electronic properties. However, even in the simplest model of spinless fermions on a two-dimensional checkerboard lattice, the quantum phase diagram as a function of nearest-neighbor interaction remains under debate. We employ constrained-path quantum Monte Carlo simulations (CP-QMC) simulations to investigate the problem using a two-dimensional torus geometry. We cross-validate our results on small lattices by comparing them with density-matrix renormalization group calculations, finding quantitative agreement. In particular, we implement an improved optimization scheme within the CP-QMC simulations, enabling the identification of a bond-nematic Dirac semimetal phase that was found in tensor-network studies on cylindrical geometries, but remains inaccessible to Hartree-Fock mean-field methods. The CP-QMC approach makes it possible to establish the emergence of this phase in a geometry that preserves lattice rotational symmetry and permits extrapolation to the thermodynamic limit. Our results show that the quantum phase diagram of spinless fermions on the checkerboard lattice with nearest-neighbor repulsion features three interaction-induced phases at half filling: a quantum anomalous Hall insulator at weak coupling, a bond-nematic Dirac semimetal at intermediate coupling, and a site-nematic insulator at strong coupling.