Emergent relativistic symmetry from interacting fermions on the honeycomb bilayer

TL;DR

This study uses large-scale quantum Monte Carlo simulations to explore how interactions in honeycomb bilayer fermions induce a continuous semimetal-insulator transition with emergent relativistic symmetry, aligning with the Gross-Neveu-Ising universality class.

Contribution

It provides the first numerical confirmation that the semimetal-insulator transition in interacting honeycomb bilayer fermions belongs to the 2+1D Gross-Neveu-Ising universality class with emergent relativistic symmetry.

Findings

Interaction induces Dirac points from quadratic band touching.

Transition is continuous with emergent relativistic symmetry.

Results match theoretical predictions for critical exponents.

Abstract

We study the phase diagram of interacting spinless fermions on the honeycomb bilayer at charge neutrality using large-scale quantum Monte Carlo simulations. In the noninteracting limit, the low-energy spectrum features quadratically dispersing bands that touch at the corners of the hexagonal Brillouin zone. Weak to intermediate interactions induce a splitting of each of the quadratic band touching points into four Dirac points, located along high-symmetry directions of the reciprocal lattice. Strong interactions lead to the formation of a layer-polarized charge density wave, which spontaneously breaks the $\mathbb Z_2$ layer inversion symmetry and opens an insulating gap in the spectrum. We show that the semimetal-to-insulator quantum phase transition as a function of interaction is continuous and characterized by emergent relativistic symmetry. Our results for the values of the correlation-length exponent $\nu$, the order-parameter anomalous dimension $\eta_\phi$, and the fermion anomalous dimension $\eta_\psi$ agree with those of the theoretically predicted 2+1D Gross-Neveu-Ising universality class with eight two-component Dirac fermions within less than 5\%\ deviation. We also determine the crossover scale as a function of interaction strength between the nonrelativistic semimetal state at high temperatures, characterized by dynamical critical exponent $z = 2$, and the Dirac semimetal state at intermediates temperatures, characterized by $z=1$. Further reducing the temperature below the crossover scale at a fixed value of the interaction strength above the quantum critical point results in a classical ordering transition in the 2D Ising universality class.