Specific heat and validity of quasiparticle approximation in the half-filled Landau level

TL;DR

This paper investigates the validity of the quasiparticle approximation in a composite fermion system at half-filled Landau level by comparing specific heat calculations from gauge field free energy and quasiparticle self-energy, finding it valid only for Coulomb interactions.

Contribution

The study provides a gauge-invariant test of the quasiparticle approximation's validity across different interaction types in the half-filled Landau level.

Findings

Quasiparticle approximation matches gauge field results only for Coulomb interaction.

The specific heat differs for non-Coulomb interactions, indicating breakdown of the approximation.

Supports the special role of Coulomb interaction in composite fermion systems.

Abstract

We calculate the specific heat of composite fermion system in the half-filled Landau level. Two different methods are used to examine validity of the quasiparticle approximation when the two-body interaction is given by $V(q) = V_0 / q^{2-\eta}$ ($1 \le \eta \le 2$). The singular part of the specific heat is calculated from the free energy of the gauge field, which is compared with the specific heat calculated from the quasiparticle approximation via the singular self-energy correction due to the gauge field fluctuations. It turns out that two results are in general different and they coincide only for the case of the Coulomb interaction ($\eta = 1$). This result supports the fact that the quasiparticle approximation is valid only for the case of the Coulomb interaction. It is emphasized that this result is obtained by looking at a gauge-invariant quantity -- the specific heat.