``Bare'' Effective Mass in Finite Sized $\nu = 1/2$ Systems

TL;DR

This paper investigates the effective mass of quasiparticles in finite-sized quantum Hall systems at filling factor 1/2, using finite size calculations and proposing a conjecture for the thermodynamic limit.

Contribution

It introduces a method to relate effective mass to response functions and provides finite size calculations for small systems, offering insights into the thermodynamic limit.

Findings

Finite size calculations for 7, 8, and 9 fermions.

Relation between effective mass and density response functions.

Conjecture on the behavior in the thermodynamic limit.

Abstract

In this note, we discuss the effective mass of quasiparticles in finite sized $\nu = 1/2$ systems in the lowest Landau level, given a natural notion we have of the Fermi surface in these finite sized systems. The effective mass is related to the difference between instantaneous density-density response functions of the ground state and excited states of the system; we do a finite size calculation for this difference for $\nu = 1/2$ systems with 7, 8 and 9 fermions, and conjecture how the difference must look in the thermodynamic limit.