Moments and multiplets in moiré materials

The observation of strongly correlated states in moiré systems has renewed the conceptual interest in magnetic systems with higher SU(4) spin symmetry, e.g., to describe Mott insulators where the local moments are coupled spin–valley degrees of freedom. Here, we discuss a numerical renormalization group scheme to explore the formation of spin–valley ordered and unconventional spin–valley liquid states at zero temperature based on a pseudo-fermion representation. Our generalization of the conventional pseudo-fermion functional renormalization group approach for $${{\mathfrak {s}}}{{\mathfrak {u}}}$$ s u (2) spins is capable of treating diagonal and off-diagonal couplings of generic spin–valley exchange Hamiltonians in the self-conjugate representation of the $${{\mathfrak {s}}}{{\mathfrak {u}}}$$ s u (4) algebra. To achieve proper numerical efficiency, we derive a number of symmetry constraints on the flow equations that significantly limit the number of ordinary differential equations to be solved. As an example system, we investigate a diagonal SU(2) $$_{\text {spin}}$$ spin $$\otimes $$ ⊗ U(1) $$_{\text {valley}}$$ valley model on the triangular lattice which exhibits a rich phase diagram of spin and valley ordered phases. Graphic Abstract