Fermion-Spin Transformation to Implement the Charge-Spin Separation

TL;DR

The paper introduces a fermion-spin transformation method to study low-dimensional t-J models, successfully separating charge and spin degrees of freedom and capturing key physical properties in one and two dimensions.

Contribution

It develops a novel fermion-spin transformation approach that satisfies local constraints and can be applied to both 1D and 2D systems, providing insights into charge-spin separation.

Findings

In 1D, the approach yields Luttinger liquid behavior with gapless excitations.

In 2D, the magnetized flux state has lowest energy at half-filling.

The method accurately reproduces correlation function exponents and electron distributions.

Abstract

A novel approach, the fermion-spin transformation to implement the charge-spin separation, is developed to study the low-dimensional $t$-$J$ model. In this approach, the charge and spin degrees of freedom of the physical electron are separated, and the charge degree of freedom is represented by a spinless fermion while the spin degree of freedom is represented by a {\it hard-core boson}. The on-site local constraint for single occupancy is satisfied even in the mean-field approximation and the sum rule for the physical electron is obeyed. This approach can be applied to both one and two-dimensional systems. In the one-dimensional case, the spinon as well as the physical electron behaves like Luttinger liquids. We have obtained a gapless charge and spin excitation spectrum, a good ground state energy, and a reasonable electron-momentum distribution within the mean-field approximation. The correct exponents of the correlation functions and momentum distribution are also obtained if the {\it squeezing} effect and rearrangement of the spin configurations are taken into account. In the two-dimensional case, within the mean-field approximation the magnetized flux state with a gap in the spinon spectrum has the lowest energy at half-filling. The antiferromagnetic long-range order is destroyed by hole doping