Elementary Excitations of One-Dimensional t-J Model with Inverse-Square Exchange

TL;DR

This paper analyzes the exact elementary excitations in a one-dimensional t-J model with inverse-square exchange, revealing fractionalized particles with specific spectral contributions due to underlying supersymmetry.

Contribution

It provides an exact characterization of excitations and spectral weights in the inverse-square exchange t-J model, highlighting the role of supersymmetric Yangian symmetry.

Findings

Identification of spinons, holons, and anti-holons with fractional statistics

Mapping of spectral weight regions in energy-momentum space

Selection rules governing spectral contributions

Abstract

We identify exact excitation content of the intermediate states for the one-particle Green's functions, spin-spin and (charge) density-density correlation functions of the periodic one-dimensional $t$-$J$ model with inverse square exchange. The excitations consist of neutral $S=1/2$ spinons and spinless (charge $-e$) holons with semionic fractional statistics, and bosonic (charge +2$e$) ``anti-holons'' which are excitations of the holon condensate. Due to the supersymmetric Yangian quantum symmetry of this model, only the excited states with {\it finite} number of elementary excitations contribute to the spectral functions. We find a set of selection rules, and this allows us to map out the regions of non-vanishing spectral weight in the energy-momentum space for the various correlation functions.