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

Tigran Zalinyan1,* and Giovanni Nastasi2,†

  • *Contact author: tigran.zalinyan@ysu.am
  • †Contact author: giovanni.nastasi@unikore.it
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Phys. Rev. B 114, 245411 – Published 13 October, 2026

DOI: https://doi.org/10.1103/d4lr-bpkb

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.

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Phys. Rev. B 114, 245411– Published 13 October, 2026
  • Received 9 April 2026
  • Revised 3 August 2026
  • Accepted 25 September 2026
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