We study the nonlinear response of nonintegrable one-dimensional (1D) spin models using infinite matrix-product state techniques. As a benchmark and demonstration of the method, we first calculate the two-dimensional (2D) coherent spectroscopy for the exactly soluble ferromagnetic transverse field Ising model where excitations are freely moving domain walls. We then investigate the distinct signatures of confined bound states by introducing a longitudinal field and observe the emergence of strong nonrephasinglike signals. To interpret the observed phenomena, we use a two-kink approximation to perturbatively compute the 2D spectra. We find good agreement in comparison with the exact results of the infinite matrix-product state method in the strongly confined regime. We discuss the relevance of our results for quasi-$1\mathrm{D}$ Ising spin chain materials, such as ${\mathrm{CoNb}}_2{\mathrm{O}}_6$.

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• Bound states
• Fractionalization
• Nonlinear optics
• Spinon
• 1-dimensional spin chains
• Matrix product states
• Terahertz time-domain spectroscopy
• Two-dimensional coherent spectroscopy