Generalized CP^1 model from t_1-t_2-J model

TL;DR

This paper derives a generalized CP^1 effective field theory from the t_1-t_2-J model, incorporating gauge invariance, Fermi quasiparticles with charge and spin, and discusses mean-field symmetry breaking and long-distance fluctuations.

Contribution

It introduces a novel generalized CP^1 model for the t_1-t_2-J system, including gauge invariance and a new parametrization of long-distance fluctuations.

Findings

Effective theory includes gauge-invariant fields and Fermi quasiparticles with charge and spin.

Mean-field analysis suggests gauge-symmetry breaking via four-fermion interactions.

Long-distance fluctuations are parametrized using gauge-invariant fields, leading to a new effective description.

Abstract

A long-wavelength, low-frequency effective theory is obtained from $t_1-t_2-J$ model. The action is written in terms of two-component bose spinor fields (CP^1 fields) and two spinless Fermi fields. The generalized CP^1 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-feild theory of a gauge-symmerty 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 $t_1-t_2-J$ model, with the help of gauge invariant fields. It is argued that the resulting Fermi quasiparticles of the $t_1-t_2-J$ model have both charge and spin. The effective action is rewritten in terms of spin 1/2 Fermi spinor, which has the charge of the holes, and unit vector.