A field-theory approach to the t-j model and the spin-charge separation

We analyze the t-J model using the CP¹ representation for the slave operators (holons and sp spinons) which is particularly suited to study the phenomenon of the spin-charge separation in strongly correlated electron systems. In particular, we show that for the one-dimensional t-J model below half-filling the low-energy effective dynamics of the spin and charge degrees of freedom is represented in the continuum limit by a CP¹ model with a topological term, minimally coupled to a massless Dirac field with a four-fermion interaction. The bosonic term of this action describes the spin waves produced by the spinons, while the fermionic term represents the low-energy charge excitations. This theory exhibits explicitly a local abelian gauge invariance.