Instantons and the spectral function of electrons in the half-filled Landau level

Abstract

We calculate the instanton-anti-instanton action $S_{M {\bar M}} (τ)$ in the gauge theory of the half-filled Landau level. It is found that $S_{M {\bar M}} (τ) = (3 - η) \left [ Ω_0 (η) \ τ\right ]^{1 / (3 - η)}$ for a class of interactions $v ({\bf q}) = V_0 / q^η \ ( 0 \leq η< 2 )$ between electrons. This means that the instanton-anti-instanton pairs are confining so that a well defined `charged' composite fermion can exist. It is also shown that $S_{M {\bar M}} (τ)$ can be used to calculate the spectral function of electrons from the microscopic theory within a semiclassical approximation. The resulting spectral function varies as $e^{ - \left [ Ω_0 (η) / ω\right ]^{1 / ( 2 - η) } }$ at low energies.