Projected electron operator (${\tilde{c}}_{i\sigma }=c_{i\sigma }(1-n_{i\bar{\sigma }})$)

An electron annihilation operator restricted to the no-double-occupancy sector of the t-J model. It removes a spin-$\sigma$ electron only when the opposite-spin site occupation vanishes. The corresponding creation operator cannot create a doubly occupied site. These projected operators do not obey the unrestricted canonical on-site fermion algebra on all states.