Quantum phase transitions of multi-species Dirac fermions

TL;DR

This study uses quantum Monte Carlo simulations to analyze how velocity modulation in multi-species Dirac fermions influences the transition from semimetal to antiferromagnetic insulator, revealing tunable critical interactions and non-monotonic magnetic order.

Contribution

It provides new insights into how Dirac cone velocities affect the interaction-driven phase transition in a modulated $ ext{pi}$-flux model, with implications for ultracold atom experiments.

Findings

Critical interaction strength $U_c$ decreases with outer Dirac cone velocity reduction.

Antiferromagnetic structure factor peaks at specific hopping modulations.

Sublattice magnetization is maximized at intermediate anisotropy in the strong coupling limit.

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.