Year: 2026
Type: article
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 $ν$, the order-parameter anomalous dimension $η_ϕ$, and the fermion anomalous dimension $η_ψ$ 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.
DOI: 10.1103/51zq-f75g
Authors: Zi Hong Liu, Lukas Janssen
Institutions: Fudan University, Technische Universität Dresden
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1993662523, G2152757567, G3374273714, G3404629221, G4001216468, Quantenkritische Materie: Von frustrierten Spins zu wechselwirkenden Fermionen und emergenten Eichfeldern, EXC 2147: Komplexität und Topologie in Quantenmaterialien (CT.QMAT), SFB 1143: Korrelierter Magnetismus: Von Frustration zu Topologie, G936330020
OpenAlex ID: W7140223749