Low-noise Pauli-consistent ensemble Monte Carlo for graphene with electron-electron scattering

TL;DR

This paper presents a novel sampled-partner approximation for ensemble Monte Carlo simulations of graphene, significantly reducing computational costs while maintaining accuracy, enabling low-noise, large-ensemble simulations.

Contribution

Introduction of a sampled-partner approximation for electron-electron scattering in Monte Carlo simulations, improving efficiency without sacrificing accuracy.

Findings

Close agreement with full-sum reference simulations.

Substantial reduction in computational cost.

Oscillatory artifacts are numerical and can be mitigated.

Abstract

We investigate Pauli-consistent ensemble Monte Carlo simulations of graphene with explicit intraband electron-electron scattering. To reduce the cost of electron-electron proposal-rate evaluation, we introduce a sampled-partner approximation that replaces the full partner-cell sum by uniform sampling from the instantaneous ensemble, while leaving the event-level collision step unchanged. Comparison with the full-sum reference shows close agreement together with a substantial reduction in computational cost, enabling large-ensemble low-noise simulations. In this regime, systematic oscillatory components become clearly resolved in ensemble-averaged time traces. We show that these oscillations are numerical and originate from deterministic drift on the discretized momentum-space grid. We also discuss a procedure for reducing their impact in recorded observables without modifying the underlying Monte Carlo dynamics.