The Lowest Landau Level Anyon Equation of State in the Anti-screening Regime

TL;DR

This paper investigates the thermodynamics of lowest Landau level anyons in the anti-screening regime, revealing how the equation of state can be analytically continued across the Fermi point and highlighting the role of non-LLL states near the Bose point.

Contribution

It introduces an analytical continuation of the LLL-anyon equation of state into the anti-screening regime and discusses the impact of non-LLL states, supported by exact 3-anyon solutions.

Findings

The LLL approximation breaks down near the Bose point due to non-LLL states.

Critical filling factors differ in screening and anti-screening regimes, approaching infinity or 1/2.

An exclusion statistics interpretation explains the observed phenomena.

Abstract

The thermodynamics of the anyon model projected on the lowest Landau level (LLL) of an external magnetic field is addressed in the anti-screening regime, where the flux tubes carried by the anyons are parallel to the magnetic field. It is claimed that the LLL-anyon equation of state, which is known in the screening regime, can be analytically continued in the statistical parameter across the Fermi point to the antiscreening regime up to the vicinity (whose width tends to zero when the magnetic field becomes infinite) of the Bose point. There, an unphysical discontinuity arises due to the dropping of the non-LLL eigenstates which join the LLL, making the LLL approximation no longer valid. However, taking into account the effect of the non-LLL states at the Bose point would only smoothen the discontinuity and not alter the physics which is captured by the LLL projection: Close to the Bose point, the critical filling factor either goes to infinity (usual bosons) in the screening situation, or to 1/2 in the anti-screening situation, the difference between the flux tubes orientation being relevant even when they carry an infinitesimal fraction of the flux quantum. An exclusion statistics interpretation is adduced, which explains this situation in semiclassical terms. It is further shown how the exact solutions of the 3-anyon problem support this scenario as far as the third cluster coefficient is concerned.