A Gauge Invariant Way to Evaluate Quasiparticle Effective Mass in Fermionic Systems with Gauge Interactions

TL;DR

This paper introduces a gauge-invariant method to compute quasiparticle effective mass in systems with gauge interactions, applying it to a model related to the half-filled Landau level, and discusses corrections beyond RPA.

Contribution

It presents a novel gauge-invariant definition of effective mass and applies it to a Landau level model, providing a systematic approach beyond RPA.

Findings

Effective mass depends only on gauge-invariant response functions.

RPA yields a finite effective mass in the model.

Organizing perturbation in powers of Λ/k_F helps study physics beyond RPA.

Abstract

In this paper, we propose a gauge-invariant way to define and calculate the effective mass for quasiparticles in systems with gauge interactions, and apply it to a model closely related to the half-filled Landau level problem. Our model is equivalent to the Halperin-Lee-Read $\nu = 1/2$ Hamiltonian with an ultraviolet cutoff $\Lambda$ for the gauge fields, and we expand our answer in powers of $\Lambda / k_F$, assuming it is small. In this definition the effective mass depends only on the gauge-invariant density and current response functions of the system. Within RPA, this definition yields a finite result for the effective mass in our model. We also comment on corrections to this effective mass formula when processes beyond RPA are included. Finally, we comment briefly on the observation that organizing the perturbation expansion in powers of $\Lambda / k_F$ is a way to systematically study the physics beyond RPA.