Comparison of the $\pi$ and $\Delta$ operator approximations for the two-dimensional t-J model

TL;DR

This paper compares two operators, $$ and $$, in the 2D t-J model, finding their spectra similar but questioning the SO(5) symmetry hypothesis.

Contribution

It provides a direct comparison of the $$ and $$ operators' spectra and weights, challenging the assumed SO(5) symmetry in the 2D t-J model.

Findings

Spectra of $$ and $$ are similar.

Weight transferred to the two-hole ground state is smaller for $$.

The results suggest the 2D t-J model lacks the claimed SO(5) symmetry.

Abstract

We compare the spectra of the new $\pi$ operator of the SO(5) theory and the conventional $\Delta$ operator for the two-dimensional t-J model. We also calculate the weight transferred to the two-hole ground state from half-filling by these operators. We find that the spectra of these operators are quite similar and the weight for the $\pi$ operator is smaller than the weight for the $\Delta$ operator. We argue that the two-dimensional t-J model does not have a good approximate SO(5) symmetry claimed in Ref. 1.