A Field Theory Approach to the $t$-$J$ Model and the Spin-Charge Separation

TL;DR

This paper employs a ${ m CP}^1$ field theory approach to analyze the $t$-$J$ model, revealing the dynamics of spin-charge separation in one-dimensional strongly correlated electron systems through a continuum effective theory.

Contribution

It introduces a ${ m CP}^1$ representation for the $t$-$J$ model that explicitly captures spin-charge separation and incorporates a topological term and gauge invariance in the effective field theory.

Findings

Low energy dynamics described by a ${ m CP}^1$ model with a topological term.

Spin and charge degrees of freedom represented by bosonic and fermionic fields.

Explicit local abelian gauge invariance in the effective theory.

Abstract

We analyze the $t$-$J$ model using the ${\rm CP}^1$ representation for the slave operators (holons and 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 ${\rm CP}^1$ 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.