# CP1|1 nonlinear sigma model vs strong electron correlations

## TL;DR

This paper derives a nonlinear sigma model on the supermanifold CP^{1|1} to describe the low-energy physics of the doped t-J model at the SUSY point, but finds it cannot fully capture strong correlation effects at finite doping.

## Contribution

It demonstrates that the canonical CP^{1|1} nonlinear sigma model fails to describe strong correlations in the doped t-J model at finite doping.

## Key findings

- The CP^{1|1} NLSM does not incorporate doping self-consistently.
- Strong correlations are not captured by the standard CP^{1|1} NLSM.
- The model's limitations highlight the need for alternative approaches.

## Abstract

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}