The layered transition metal dichalcogenide $1\text{T-TiS}{\mathrm{e}}_2$ is of great research interest, having intriguing properties of charge density waves (CDWs) and superconductivity under doping or pressure. The monolayer form of $1\text{T-TiS}{\mathrm{e}}_2$ also shows a CDW with a higher transition temperature than the bulk, indicating a stronger CDW interaction. By using the meta-generalized gradient approximation (metaGGA)-based model Bethe-Salpeter equation (mBSE) and many-body perturbation GW+BSE methods, we calculate the exciton binding energies and electron energy loss spectrum (EELS) for the $1\text{T-TiS}{\mathrm{e}}_2$ monolayer under different in-plane biaxial strains. We find that even without strain the $1\text{T-TiS}{\mathrm{e}}_2$ monolayer can have negative exciton energies at the Brillouin zone boundary point M, with a binding energy larger than the gap. The calculated EELS reinforces this picture, indicating exciton insulator (EI) states in $1\text{T-TiS}{\mathrm{e}}_2$ monolayer even without strain. The Wannier-Mott formula calculations of exciton binding energy corroborate results from GW+BSE. Small compressive strain enhances the EI state, and for tensile strains slightly less than 3%, the EI state in this monolayer persists. At large tensile strains, the material makes a transition to a normal semiconductor. Our results provide important information for understanding the quantum nature of this two-dimensional material. Our results from the standard ${\mathrm{G}}_0{\mathrm{W}}_0$@PBE+SOC+U+BSE approach are not qualitatively different from those of a more computationally efficient metaGGA-based $\mathrm{SCAN}+\mathrm{SOC}+\mathrm{U}+\mathrm{mBSE}+f_{xc}^{\mathrm{loc}}$ approach that employs a model BSE.

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• Charge density waves
• Electronic structure
• Excitons
• First-principles calculations