Advancing Tensor Network Approaches to Excitations in Frustrated Magnets

While many analytical and numerical techniques have explored ground-state properties of frustrated magnets, methods for accessing excitations remain underdeveloped. We develop tensor network methods to study spin excitations in frustrated quantum magnets on the triangular lattice. Building on variational iPEPS techniques, we construct momentum-resolved excited states using tangent-space and quasiparticle ansatz. A key idea is to compute real-space components of the quasiparticle ansatz on a finite patch, enabling efficient Fourier transforms to arbitrary momenta. Benchmarking against spin-wave and DMRG results, our approach captures both magnon and continuum features across different regimes of the XXZ and J1-J2 models. These results demonstrate how tensor networks can now quantitatively resolve excitation spectra in strongly correlated two-dimensional systems beyond conventional analytical mean-field methods and finite-size numerical methods.