Microscopic details of two-dimensional spectroscopy of one-dimensional quantum Ising magnets

The identification of microscopic systems describing the low-energy properties of correlated materials has been a central goal of spectroscopic measurements. We demonstrate how two-dimensional (2D) nonlinear spectroscopy can be used to distinguish effective spin systems whose linear responses show similar behavior. Motivated by recent experiments on the quasi-1D Ising magnet CoNb2O6, we focus on two proposed systems- the ferromagnetic twisted Kitaev spin chain with bond dependent interactions and the transverse field Ising chain. The dynamical spin structure factor probed in linear response displays similar broad spectra for both systems from their fermionic domain wall excitations. In sharp contrast, the 2D nonlinear spectra of the two systems show clear qualitative differences: those of the twisted Kitaev spin chain contain off-diagonal peaks originating from the bond dependent interactions and transitions between different fermion bands absent in the transverse field Ising chain. We discuss the different signatures of spin fractionalization in integrable and nonintegrable regimes of the systems and their connection to experiments.