Mass-Zero constrained dynamics and statistics for the shell model in magnetic field

TL;DR

This paper introduces the Mass-Zero (MaZe) constrained dynamics method for efficiently simulating systems with auxiliary variables, ensuring exact physical dynamics and sampling, especially in magnetic fields.

Contribution

The paper extends the MaZe method to handle semiholonomic constraints involving velocities, applicable to systems in magnetic fields, with a proof-of-principle application to NaCl.

Findings

MaZe provides exact Born-Oppenheimer dynamics.

MaZe ensures exact sampling of physical probability densities.

Extension to semiholonomic constraints broadens applicability.

Abstract

In several domains of physics, including first principle simulations and classical models for polarizable systems, the minimization of an energy function with respect to a set of auxiliary variables must be performed to define the dynamics of physical degrees of freedom. In this paper, we discuss a recent algorithm proposed to efficiently and rigorously simulate this type of systems: the Mass-Zero (MaZe) Constrained Dynamics. In MaZe the minimum condition is imposed as a constraint on the auxiliary variables treated as degrees of freedom of zero inertia driven by the physical system. The method is formulated in the Lagrangian framework, enabling the properties of the approach to emerge naturally from a fully consistent dynamical and statistical viewpoint. We begin by presenting MaZe for typical minimization problems where the imposed constraints are holonomic and summarizing its key formal properties, notably the exact Born-Oppenheimer dynamics followed by the physical variables and the exact sampling of the corresponding physical probability density. We then generalize the approach to the case of conditions on the auxiliary variables that linearly involve their velocities. Such conditions occur, for example, when describing systems in external magnetic field and they require to adapt MaZe to integrate semiholonomic constraints. The new development is presented in the second part of this paper and illustrated via a proof-of-principle calculation of the charge transport properties of a simple classical polarizable model of NaCl.