Slave Anyons in the $t$-$J$ Model at the Supersymmetric Point

TL;DR

This paper explores the supersymmetric $t$-$J$ model using slave anyon operators, revealing that holons and spinons can exhibit arbitrary anyonic statistics and demonstrating the model's $SU(1|2)$ invariance at a specific coupling.

Contribution

It introduces a generalized abelian bosonization for the 2D $t$-$J$ model and explicitly constructs the superalgebra $SU(1|2)$ within the slave anyon framework.

Findings

Holons and spinons can be anyons with arbitrary complementary statistics.

The braiding properties of slave anyons are thoroughly characterized.

The $t$-$J$ Hamiltonian is invariant under $SU(1|2)$ at $J=2t$.

Abstract

We discuss the properties of the supersymmetric $t$-$J$ model in the formalism of the slave operators. In particular we introduce a generalized abelian bosonization for the model in two dimensions, and show that holons and spinons can be anyons of arbitrary complementary statistics (slave anyon representation). The braiding properties of these anyonic operators are thoroughly analyzed, and are used to provide an explicit linear realization of the superalgebra $SU(1|2)$. Finally, we prove that the Hamiltonian of the $t$-$J$ model in the slave anyon representation is invariant under $SU(1|2)$ for $J=2\,t$.