Spectral flow in the supersymmetric $t$-$J$ model with a $1/r^2$ interaction

TL;DR

This paper investigates the spectral flow in the supersymmetric t-J model with 1/r^2 interaction, revealing how charge and spin sectors behave under twisted boundary conditions and how fractional exclusion statistics manifest at half filling.

Contribution

It provides an exact analysis of spectral flow in the supersymmetric t-J model, connecting the results to the motif picture and fractional exclusion statistics.

Findings

Spectral flow fits the motif picture in the asymptotic Bethe ansatz.

Fractional exclusion statistics appear at half filling.

Doping obscures fractional exclusion statistics due to incommensurability.

Abstract

The spectral flow in the supersymmetric {\it t-J} model with $1/r^2$ interaction is studied by analyzing the exact spectrum with twisted boundary conditions. The spectral flows for the charge and spin sectors are shown to nicely fit in with the motif picture in the asymptotic Bethe ansatz. Although fractional exclusion statistics for the spin sector clearly shows up in the period of the spectral flow at half filling, such a property is generally hidden once any number of holes are doped, because the commensurability condition in the motif is not met in the metallic phase.