Variational wave functions constitute a precious tool for the study of frustrated spin models, which represent a formidable challenge for most numerical methods. In this talk, we discuss how magnetic and nonmagnetic phases of spin systems can be described by Gutzwiller-projected fermionic wave functions, drawing examples from a recent study of the Heisenberg model on the square-kagome lattice [1]. We then show how dynamical spectra can be obtained by suitable variational Ansätze for excited states. The analysis of the dynamical structure factor of two highly frustrated systems allows us to show how gapless spin liquid states become trivial insulators on cylindrical geometries [2].
[1] N. Astrakhantsev, F. Ferrari, N. Niggemann et al, PRB 104, L220408 (2021)
[2] F. Ferrari, A. Parola, F. Becca, PRB 103, 195140 (2021)