We perform a systematic study on the effects of electric fields in the Luttinger liquid phase of the one-dimensional spin-$1/2 K_1{J}_1{\mathrm{\Gamma }}_1{\mathrm{\Gamma }}_1^{\prime }{K}_2{J}_2$ model in the region of ferromagnetic nearest-neighboring Kitaev coupling. We find that while electric fields along (1,1,1) direction maintain the Luttinger liquid behavior, fields along other directions drive the system to a dimerized state. An estimation is made on how effective a (1,1,1) field is for tuning the Luttinger parameter in real materials. Our work is useful for understanding the effects of electric fields in one-dimensional generalized Kitaev spin models, and provides a starting point for exploring the electric-field-related physics in two dimensions based on a quasi-one-dimensional approach.

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• Magnetism
• Magnetic systems
• Density matrix methods
• Luttinger liquid model
• Many-body techniques