Grand-canonical Monte-Carlo simulation methods for charge-decorated cluster expansions

TL;DR

This paper introduces two novel Monte Carlo methods for simulating charge-decorated lattice models under charge balance constraints, enabling more efficient sampling of charged crystalline systems.

Contribution

It proposes the table-exchange and square-charge bias methods for grand-canonical Monte Carlo sampling with charge constraints, advancing simulation techniques for charged materials.

Findings

Both methods improve sampling efficiency in charge-constrained systems.

Parameter tuning affects the effectiveness of the algorithms.

Practical strategies are provided for real-world applications.

Abstract

Monte-Carlo sampling of lattice model Hamiltonians is a well-established technique in statistical mechanics for studying the configurational entropy of crystalline materials. When species to be distributed on the lattice model carry charge, the charge balance constraint on the overall system prohibits single-site Metropolis exchanges in MC. In this article, we propose two methods to perform MC sampling in the grand-canonical ensemble in the presence of a charge-balance constraint. The table-exchange method (TE) constructs small charge-conserving excitations, and the square-charge bias method (SCB) allows the system to temporarily drift away from charge neutrality. We illustrate the effect of internal hyper-parameters on the efficiency of these algorithms and suggest practical strategies on how to apply these algorithms to real applications.