Spin Susceptibility and Gap Structure of the Fractional-Statistics Gas

TL;DR

This study investigates the spin susceptibility and gap structure of a fractional-statistics gas, revealing how interactions significantly lower the spin gap and confirming the validity of the approximation methods used.

Contribution

It introduces procedures to determine electron energy gaps in high-temperature superconductors using fractional statistics models, and analyzes the spin susceptibility spectrum of a fractional-statistics gas.

Findings

Interactions reduce the spin gap to about 0.2 ± 0.2 ħω_c.

Lower Landau levels remain visible but broadened and shifted.

Approximation methods agree well with exact results for the non-interacting Bose gas.

Abstract

This paper establishes and tests procedures which can determine the electron energy gap of the high-temperature superconductors using the $t\!-\!J$ model with spinon and holon quasiparticles obeying fractional statistics. A simpler problem with similar physics, the spin susceptibility spectrum of the spin 1/2 fractional-statistics gas, is studied. Interactions with the density oscillations of the system substantially decrease the spin gap to a value of $(0.2 \pm 0.2)$ $\hbar \omega_c$, much less than the mean-field value of $\hbar\omega_c$. The lower few Landau levels remain visible, though broadened and shifted, in the spin susceptibility. As a check of the methods, the single-particle Green's function of the non-interacting Bose gas viewed in the fermionic representation, as computed by the same approximation scheme, agrees well with the exact results. The same mechanism would reduce the gap of the $t\!-\!J$ model without eliminating it.