Antiferromagnetic transitions of Dirac fermions in three dimensions

Abstract

We use determinant quantum Monte Carlo (DQMC) simulations to study the role of electron-electron interactions on three-dimensional (3D) Dirac fermions based on the $\pi$-flux model on a cubic lattice. We show that the Hubbard interaction drives the 3D Dirac semimetal to an antiferromagnetic (AF) insulator only above a finite critical interaction strength and the long-ranged AF order persists up to a finite temperature. We evaluate the critical interaction strength and temperatures using finite-size scaling of the spin structure factor. The critical behaviors are consistent with the (3+1)d Gross-Neveu universality class for the quantum critical point and 3D Heisenberg universality class for the thermal phase transitions. We further investigate correlation effects in birefringent Dirac fermion system. It is found that the critical interaction strength $U_c$ is decreased by reducing the velocity of the Dirac cone, quantifying the effect of velocity on the critical interaction strength in 3D Dirac fermion systems. Our findings unambiguously uncover correlation effects in 3D Dirac fermions, and may be observed using ultracold atoms in an optical lattice.

10 pages, 10 figures

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Cited by in corpus (7)

• SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions (version 2.0 release)
• Emergent chiral symmetry in a three-dimensional interacting Dirac liquid
• Yukawa-Lorentz symmetry of interacting non-Hermitian birefringent Dirac fermions
• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
• Emergent Anti-ferromagnetism in a Y -Shaped Kekulé Graphene
• Emergent soft-gap Anderson models at quantum criticality in a lattice Hamiltonian within dynamical mean field theory
• Axionic quantum criticality of generalized Weyl semimetals