# Effective mass of quasiparticles from thermodynamics

## TL;DR

This paper explores calculating the effective mass of quasiparticles from thermodynamic free energy, comparing it with traditional methods, and discusses discrepancies and potential issues in quantum Monte Carlo data interpretations.

## Contribution

It proposes a thermodynamic approach to determine quasiparticle effective mass and analyzes inconsistencies in existing quantum Monte Carlo data.

## Key findings

- Quantum Monte Carlo estimates align with many-body theory results.
- Parametrized quantum Monte Carlo data show unphysical negative entropy at low densities.
- Discrepancies may stem from how exchange energy is treated at finite temperature.

## Abstract

We discuss the potential advantages of calculating the effective mass of quasiparticles in the interacting electron liquid from the low-temperature free energy vis-a-vis the conventional approach, in which the effective mass is obtained from approximate calculations of the self-energy, or from a quantum Monte Carlo evaluation of the energy of a variational "quasiparticle wave function". While raw quantum Monte Carlo data are presently too sparse to allow for an accurate determination of the effective mass, the values estimated by this method are numerically close to the ones obtained in previous calculations using diagrammatic many-body theory. In contrast to this, a recently published parametrization of quantum Monte Carlo data for the free energy of the homogeneous electron liquid yields effective masses that considerably deviate from previous calculations and even change sign for low densities, reflecting an unphysical negative entropy. We suggest that this anomaly is related to the treatment of the exchange energy at finite temperature.