Linear scaling electronic structure calculations and accurate sampling with noisy forces

TL;DR

This paper introduces a new statistical method for electronic structure calculations that scales linearly with system size, enabling efficient and accurate simulations of large systems, including metals, by handling noisy forces effectively.

Contribution

The paper presents a novel linear-scaling approach for electronic structure calculations based on exact fermionic determinant decomposition and field theory mapping, improving efficiency and applicability.

Findings

Achieves linear scaling in force evaluations for large systems.

Handles noisy forces accurately in sampling the Boltzmann distribution.

Applicable to diverse fields like quantum chromodynamics and colloidal physics.

Abstract

Numerical simulations based on electronic structure calculations are finding ever growing applications in many areas of physics. A major limiting factor is however the cubic scaling of the algorithms used. Building on previous work [F. R. Krajewski and M. Parrinello, Phys.Rev. B71, 233105 (2005)] we introduce a novel statistical method for evaluating the inter-atomic forces which scales linearly with system size and is applicable also to metals. The method is based on exact decomposition of the fermionic determinant and on a mapping onto a field theoretical expression. We solve exactly the problem of sampling the Boltzmann distribution with noisy forces. This novel approach can be used in such diverse fields as quantum chromodynamics, quantum Monte Carlo or colloidal physics.