Quantifying the fragility of unprotected quadratic band crossing points

TL;DR

This paper investigates the stability of quadratic band crossing points in an interacting fermion lattice model, revealing their inherent fragility due to interaction effects and dispersion renormalizations, supported by perturbative analysis and quantum Monte Carlo simulations.

Contribution

It provides a quantitative analysis of the fragility of QBCPs under interactions, combining perturbation theory and quantum Monte Carlo methods to understand their instability.

Findings

QBCPs are fragile against dispersion renormalization due to interactions.

A nonzero interaction threshold is required for charge-density-wave instability.

Quantum Monte Carlo confirms the perturbative predictions about QBCP fragility.

Abstract

We examine a basic lattice model of interacting fermions that exhibits quadratic band crossing points (QBCPs) in the non-interacting limit. In particular, we consider spinless fermions on the honeycomb lattice with nearest neighbor hopping $t$ and third-nearest neighbor hopping $t''$, which exhibits fine-tuned QBCPs at the corners of the Brillouin zone for ${t'' = t/2}$. In this situation, the density of states remains finite at the Fermi level of the half-filled band and repulsive nearest-neighbor interactions $V$ lead to a charge-density-wave (CDW) instability at infinitesimally small $V$ in the random-phase approximation or mean-field theory. We examine the fragility of the QBCPs against dispersion renormalizations in the ${t\mbox{-}t''\mbox{-}V}$ model using perturbation theory, and find that the $t''$-value needed for the QBCPs increases with $V$ due to the hopping renormalization. However, the instability toward CDW formation always requires a nonzero threshold interaction strength, i.e., one cannot fine-tune $t''$ to recover the QBCPs in the interacting system. These perturbative arguments are supported by quantum Monte Carlo simulations for which we carefully compare the corresponding threshold scales at and beyond the QBCP fine-tuning point. From this analysis, we thus gain a quantitative microscopic understanding of the fragility of the QBCPs in this basic interacting fermion system.