Dimensional reduction of U(1)\times SU(2) Chern-Simons bosonization: application to the t-J model

TL;DR

This paper develops a dimensional reduction of $U(1) imes SU(2)$ Chern-Simons bosonization, applying it to the $t-J$ model, revealing a semionic spin-charge separation that reproduces key correlation behaviors in 1D.

Contribution

It introduces a novel semionic spin-charge separation framework via dimensional reduction of Chern-Simons bosonization for the $t-J$ model.

Findings

Mean field theory reproduces large-distance correlation functions.

Semionic fields obeying braid statistics are essential for accurate modeling.

Captures the physical properties of the 1D $t-J$ model at large scales.

Abstract

We perform a dimensional reduction of the $U(1)\times SU(2)$ Chern--Simons bosonization and apply it to the $t-J$ model, relevant for high $T_c$ superconductors. This procedure yields a decomposition of the electron field into a product of two ``semionic" fields, i.e. fields obeying abelian braid statistics with statistics parameter $\theta={1\over 4}$, one carrying the charge and the other the spin degrees of freedom. A mean field theory is then shown to reproduce correctly the large distance behaviour of the correlation functions of the 1D $t-J$ model at $t>>J$. This result shows that to capture the essential physical properties of the model one needs a specific ``semionic" form of spin--charge separation.