Exploring order-to-order transitions of Dirac fermions in the regime of strong interactions

In recent years, there has been a growing interest in direct and continuous quantum phase transitions between ordered phases that do not conform with the Landau-Ginzburg paradigm. It has since been a challenge to identify models that host such transitions.
One model of interest consists of interacting Dirac fermions coupled to a transverse-field Ising model on the honeycomb lattice. It has been suggested that there is an order-to-order transition between the competing antiferromagnetic (AFM) and Ising ordered phases of this model [1].
However, the quantum Monte Carlo simulations employed were restricted to relatively small system sizes so that finite-size effects remain an issue. In the strongly interacting regime, this system can be described by an effective quantum spin model of coupled Heisenberg and Ising spins.
Within this setting, highly efficient quantum Monte Carlo methods available for spin systems can be used to drastically improve on the precision of the original fermionic estimates. In our simulations, we resolve a narrow coexistence region between the Ising and AFM-ordered phases, in contrast to the direct single transition proposed in Ref. [1].

[1] T. Sato, M. Hohenadler, and Fakher F. Assaad, PRL 119, 197203(2017)