Quantum phase transitions of multi-species Dirac fermions

Abstract

We use the determinant Quantum Monte Carlo method (DQMC) to study the interaction-driven semimetal to antiferromagnetic insulator transition in a $\pi$-flux Hamiltonian with modulated hoppings, a model which has two species of Dirac fermions. It is found that the critical interaction strength $U_c$ is decreased by reducing the velocity of the outer Dirac cone, while the inner cone velocity fixes the band width. Although $U_c$ is monotonic, at fixed inverse temperature $\beta$ the antiferromagnetic (AF) structure factor has a maximum as a function of the hopping modulation. We also study the corresponding strong coupling (Heisenberg model) limit, where the sublattice magnetization is enhanced by the alternation of the exchange couplings. The AF order is shown to be non-monotonic, and maximal at an intermediate degree of anisotropy, in qualitative agreement with the Hubbard model. These results quantify the effect of the velocities on the critical interaction strength in Dirac fermion systems and enable an additional degree of control which will be useful in studying strong correlation physics in ultracold atoms in optical lattices.

5 pages, 5 figures

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• Charge-Density Wave Order on a $\pi$-flux Square Lattice
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• Antiferromagnetic transitions of Dirac fermions in three dimensions
• Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model
• Relativistic non-Fermi liquid from interacting birefringent fermions: A robust superuniversality
• Yukawa-Lorentz symmetry of interacting non-Hermitian birefringent Dirac fermions
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• Emergent Anti-ferromagnetism in a Y -Shaped Kekulé Graphene
• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
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