Excitation spectrum and effective mass of the even-fraction quantum Hall liquid

TL;DR

This study investigates the excitation spectrum and effective mass of the even-fraction quantum Hall liquid using exact diagonalization, revealing a shell structure, a zero-gap metallic state, and deviations from simplified models.

Contribution

It provides detailed numerical analysis of the excitation spectrum, showing a shell structure and effective mass behavior in the even-fraction quantum Hall system, with deviations from existing approximations.

Findings

Spectrum exhibits shell structure matching free composite fermions

Zero excitation gap indicates a metallic state in the thermodynamic limit

Effective mass increases at certain filling factors and shows deviations from simple models

Abstract

To probe the nature of the even-fraction quantum Hall system, we have investigated the low-lying excitation spectrum by means of exact diagonalization for finite systems. We have found (i) a striking one-to-one correspondence (i.e., a shell structure) between the spectrum and those for free (composite) fermions, (ii) a surprisingly straight scaling plot for the excitation energy that gives a zero gap (metal) in the thermodynamic limit, (iii) the effective mass evaluated from the scaling becoming heavier for filling factor = 1/2, 1/4, 1/6, but (iv) some deviations from the single-mode or the Hartree-Fock composite fermion approximation as well.