The nonlinear sigma model targeted on the coset supermanifold $CP^{ 1|1}=SU(2|1)/U(1|1)$ is derived in an attempt to describe the quasiclassical low-energy effective action for the doped $t-J$ model at the SUSY point, $J=2t.$ In spite of the fact that the supermanifold $CP^{ 1|1}$ indeed appears as the phase space of the strongly correlated electrons, the canonical $CP^{ 1|1}$ nonlinear sigma model (NLSM) is unable to capture the physics of strong correlations displayed by the SUSY $t-J$ model at any finite doping. This is due to the fact that, in this regime, the doping itself cannot be self-consistently incorporated into the $CP^{ 1|1}$ NLSM. \end{ abstract}
Categories: cond-mat.str-el hep-th