Altermagnetic quantum criticality: the role of the sublattice degrees of freedom

Altermagnets (AM) are magnetic phases with nodal spin-splitting of their band structure and zero net-magnetization, in which oppositely spin-polarized sublattices are related by a rotation. The essential role that sublattice degrees of freedom play in realizing altermagnetism should also affect the electronic interactions mediated by AM fluctuations, which are particularly strong near a quantum critical point (QCP). Here, we investigate the nature of the dynamics of AM quantum critical fluctuations considering a prototypical two-sublattice AM system: the Lieb lattice with nearest and next-nearest neighbor hopping. We use a Hertz-Millis approach to couple low-energy fermions to the quantum critical modes and compute the electronic and bosonic self-energies across a wide frequency range, revealing the key role played by sublattice degrees of freedom in promoting novel quantum critical phenomena.