Effective Hamiltonians for Linear and Nonlinear Responses in Quantum Magnets

Quantum materials represent a broad class of systems whose experimental response relies on uniquely quantum aspects such as entanglement, Berry phases, and electronic correlations. Modeling of such materials presents challenges related to a variety complex behaviours that manifest at different energy scales. In this field, first-principles approaches often provide a vital bridge between experiments and theoretical models. In this talk, I will introduce our numerical strategies for systematically building low-energy models with local charge, spin, and orbital degrees of freedom of arbitrary complexity. I will discuss the insights that these methods have yielded for layered vdW materials, in which spin-orbit coupling induces strongly anisotropic and competing magnetic interactions. I will also discuss preliminary work on extending these methods to treat (i) spin-lattice coupling, and (ii) dynamical effective Hamiltonians for modeling non-linear optical responses in quantum materials, and touch on the breadth of opportunities for non-linear spectroscopy.