Dirac points and topological phases in correlated altermagnets

We explore a two-dimensional Hubbard model adapted to host altermagnetic states. Utilizing Hartree-Fock (HF) and dynamical mean-field theory (DMFT), we uncover that the magnetic solutions of this model feature Dirac points in their spectrum. HF predicts a gap opening at a critical interaction strength, a result corroborated by DMFT calculations at zero temperature. However, at finite temperature and high interaction strengths, Dirac points re-emerge at high energies in the spectral function, even if they are absent in the noninteracting and HF-predicted band structures. Analytical arguments reveal that this phenomenon arises near Mott insulating solutions from the frequency dependence of the self-energy, a behavior not captured by static mean-field theory. We identify distinctive dynamical signatures of correlated altermagnetic states in the spin-resolved optical conductivity, notably a double-peak structure likely linked to high-energy Dirac conelike bands. Moreover, the spin-resolved response exhibits spin-selective activation at different photon energies, pointing to potential applications in spin-dependent optical control. We also propose perturbations to the model that can induce a topological gap in the spectrum, leading to a transition from topologically trivial to nontrivial states by varying doping, interaction strength, and temperature.