Generalized CP1 model from the t1-t2-Jmodel

A long-wavelength, low-frequency, effective theory is obtained from the t₁-t₂-J model. The action is written in terms of two-component bose spinor fields (CP¹ fields) and two spinless Fermi fields. The generalized CP¹ model is invariant under U(1) gauge transformations. The bose fields and one of the Fermi fields have charge +1 while the other Fermi field has charge -1 with respect to these transformations. A simple mean-field theory of a gauge-symmetry breaking, based on a four-fermion interaction, is discussed. An effective theory of frustrated antiferromagnetism is obtained integrating out the Fermi fields around the mean fields. Another option is used to parametrize the long-distance fluctuations in the t₁-t₂-J model, with the help of gauge-invariant fields. It is argued that the resulting Fermi quasiparticles of the t₁-t₂-J model have both charge and spin. The effective action is rewritten in terms of the spin 12 Fermi spinor, which has the charge of the holes, and unit vector.