Session S45: Computational Methods for Statistical Mechanics: Advances and Applications II

Progress in stochastic coupled Molecular Dynamics and Spin Dynamics

Coupled Molecular Dynamics and Spin Dynamics display very attractive features that allow to get new insights of the intriguing interplay between structure and magnetism in Fe-based alloys.
Each atom is treated as a moving particle, eventually charged, supporting a classical spin.
Coordinate dependent on both magnetic exchange and magnetic anisotropic functions ensure minimal coupling between the spin and the lattice degrees of freedom to translate the well known magneto-elastic behavior of magnetic materials.
These functions need well crafted magnetic and mechanical Hamiltonian parametrized on ab-initio calculations to recover the size dependence of the energy barriers and characteristic time scales of the magnetization relaxation of condensed phases.
The equations of motion (eoms) come naturally from the Nambu dynamics that formulates covariant Poisson brackets for classical fields that encode the constrained structure of the topological space of spins.
To solve these coupled eoms in practical simulations, numerical integration algorithms based on decomposition methods have to be considered, that preserve the structure of the flow of canonical variables in such an extended phase space.
Consequences of such schemes will be discussed in details from the point of view of the known invariant quantities.
To mimic experimental conditions, various statistical ensembles have to be generated to monitor the physical properties by varying external temperature for instance, as a stochastic connection.
One consequence is that the positions, momenta and spins of all the atoms become, in return, varying quantities evolving through stochastic instead of deterministic differential equations of motion.
The challenge to compute these quantities in parallel and examples provided by the SPIN package in the open source LAMMPS code are discussed.
  

Quantum-accurate multiscale modeling of ramp compressions and magneto-elastic phase transitions in iron

Magnetic spin fluctuations have a significant impact on the thermodynamic properties of magnetic metals. Accurately predicting magneto-structural phase transitions in compressed iron hence requires accounting for those effects.
We achieved this by constructing a magneto-elastic Hamiltonian. Following the Spectral Neighbor Analysis Potential approach, a machine-learning interatomic potential for iron was trained on ab initio calculations performed on the pressure and temperature range of interest. This potential was combined to a magnetic Hamiltonian accounting for transverse and longitudinal spin fluctuations.
Leveraging the numerical capability combining lattice and magnetic degrees of freedom that was recently implemented in LAMMPS, large scale spin-lattice simulations of ramp compressions and phase transitions in iron are performed based on the developed Hamiltonian.   

Absolute entropy calculation from liquid state correlation functions

Because entropy is a function of thermodynamic state it can be determined without need for thermodynamic integration. Concepts from information theory relate the entropy of a liquid metal to its correlation functions, which can be accurately determined from ab-initio molecular dynamics. This relationship is equivalent to the "S2" method that has previously been applied to model liquids. We demonstrate the accuracy of the approach by calculating the absolute entropy of liquid aluminum entirely from first principles, and demonstrate excellent
agreement with experimental data.   

Absolute free energies from ab-initio calculation: application to phase stability of liquid metal alloys

Absolute liquid state entropies calculated using the "S2" method can be combined with ab-initio enthalpies to predict absolute Gibbs free energies. We apply this method to model the phase behavior of the liquid alkali metal alloy Li-Na, which is known to phase separate, compared with Na-K, which exhibits a eutectic. Our ab-initio simulations employ hybrid Monte Carlo/molecular dynamics to accelerate sampling of the ensemble and provide accurate pair correlation functions for the entropy calculation. Both alloys exhibit effective unlike-atom repulsion, but the weaker repulsion of Na-K allows an entropically stabilized eutectic, while the stronger repulsion of Li-Na overwhelms the entropy below a high temperature critical point which we approximately locate.   

Investigation of Fe by means of atomistic spin dynamics coupled with ab initio molecular dynamics simulations

Ab initio molecular dynamics (AIMD) is a mature approach for the investigation of nonmagnetic materials. Magnetism in condensed matter, however, introduces a further challenge for the theoretical community. A recently developed method that allows to take advantage of the accuracy of AIMD and couples the magnetic and vibrational degrees of freedom is the atomistic spin dynamics - ab initio molecular dynamics (ASD-AIMD) method [1]. In this approach, the atomic and magnetic dynamics are run in parallel while communicating with each other. The applicability of the method has been shown in the study of CrN, a semiconducting system with well localized magnetic moments.
Here, we employ ASD-AIMD simulations to investigate Fe near its Curie temperature. Being Fe a ferromagnetic metal, temperature induces fluctuations not only on the transversal magnetic degrees of freedom, but also on the longitudinal ones, which are often considered irrelevant for a system like bcc Fe. In our simulations we include this type of excitations through a mean-field entropic term, and we compare results in absence of this effect. This work is a pre-step in the calculation of free energy differences in magnetic systems with ab initio accuracy.
[1] Stockem et al., Physical Review Letters 121, 125902 (2018)   

Spin dynamics simulations on Surface for a nanoscale Heisenberg antiferromagnet

Monte Carlo and spin dynamics techniques with fourth-order
Suzuki-Trotter decompositions of the exponential operator have been
used to perform large-scale simulations of the dynamic behavior of a
nanoscale, classical, Heisenberg antiferromagnet on a simple-cubic lat-
tice at a temperature below the Néel temperature 1. A classical isotropic
Heisenberg model with an antiferromagnetic nearest-neighbor exchange
interaction was studied. A simple-cubic lattices with free boundary con-
ditions was used. The assumption of q-space spin-wave reflections with
broken momentum conservation due to free-surface confinements was
developed and used to explain multiple excitation peaks for wave vec-
tors within the first Brillouin zone appear in the spin-wave spectra of
the transverse component of dynamic structure factor in the
nanoscale classical Heisenberg antiferromagnet. In this study, we applied
the same simulation techniques to the nanoscale classical Heisenberg an-
tiferromagnet we studied before for studying spin dynamic behavior on
the surfaces of a nanoscale antiferromagnet.

1 Z.Hou, D. P. Landau, G. M. Stocks, and G. Brown, Phys.Rev.B 91, 064417(2015)   

Effective diffusion in rough potential energy landscapes

Diffusion in spatially rough, confining, one-dimensional energy landscapes is treated using Zwanzig's proposed formalism, which is based upon the Smoluchowski Equation. Disagreement between its predictions and the results of numerical simulations is observed. We use the configurational partition function to amend Zwanzig's formalism, and resolve the disagreement. The analogous over-damped Langevin Equation is proposed, and a numerical simulation scheme offering potentially significant reductions in computational time is derived. The case of random roughness is treated. We then extend the above into higher dimensions and calculate effective diffusion coefficients for motion in non-confining, rough, multi-dimensional potential energy landscapes. This leads us to propose an expression for the mean first-passage time from one potential minimum to any one of the immediately adjacent potential minima. As before, simulation schemes offering significant improvements upon those derived from the unmodified Langevin Equation are obtained. Good agreement between our theory's predictions and both numerical simulation schemes - unmodified and modified - is observed.   

Stefan–Maxwell diffusivities extracted from molecular dynamics simulations via Onsager’s regression hypothesis

We report on our development of a method to measure macroscopic diffusion coefficients in silico by analysing molecular-dynamics (MD) data. Application of Onsager’s regression hypothesis to the macroscopic constitutive laws for multicomponent Stefan–Maxwell mass transport allows application of Casimir’s fluctuation theory, which shows how the decay rates of certain autocorrelation functions relate to macroscopic mutual diffusivities. The autocorrelation functions are then determined numerically, using periodic MD simulations in the Gibbs ensemble. As an illustrative example, we compute the diffusivities for a ternary Lennard–Jones gas mixture, a case where the diffusivities measured by MD can be compared to diffusivities determined analytically by the Chapman–Enskog kinetic theory. The ultimate application of this method will be to quantify component activities and transport properties in liquids, with the ultimate aim of studying electrochemical transport properties in electrolytic solutions.   

Machine Learning the Effective Hamiltonian in High Entropy Alloys with Large DFT Datasets

The development of machine learning sheds new light on the Monte Carlo simulation of complex alloys. One major challenge, however, is that machine learning models are generally data-hungry, while the data from density functional theory (DFT) are computationally expensive. To solve this problem, we use the atomic local energy as the target variable, and harness the power of the linear-scaling DFT method to obtain large DFT data sets. This method is used to calculate the energy data of a range of MoNbTaW refractory high entropy alloys, with machine learning techniques including kernel ridge regression, Gaussian process, and artificial neural network applied to construct the effective Hamiltonian. The results demonstrate that machine learning model built on the configurational space, which naturally incorporates non-linear and multi-site interactions, can efficiently and accurately predict the DFT energy.   

Quantifying the disassembly of viral capsids from a multiscale molecular simulation approach

Molecular simulation of large biological systems, such as viral capsids, remains a challenging task in soft matter research. On one hand, coarse-grained (CG) models attempt to make feasible the description of the entire viral capsids. On the other hand, novel development of molecular dynamics (MD) simulation approaches, like enhance sampling which attempt to overcome the time scales required in biophysics. Those methods have a potential for delivering molecular structures and properties of biological systems. Nonetheless, exploring the process on how a capsid disassembles by all-atom MD simulations has been rarely attempted. Here, we propose a methodology to analyze the disassembly process of viral capsids quantitatively. In particular, we look at the effect of pH and charge of the genetic material inside the capsid, and compute the free energy of a disassembly trajectory by combining CG simulatiosn to a Poisson-Boltzmann solver. We employ such multiscale approach on the triatoma virus as a test case, and find that even though an alkaline environment enhances the stability of the capsid, the resulting deprotonation of the internal solvent generates an electrostatic repulsion that triggers disassembly   

Exploring the Potential of Parallel-Biasing in Flat Histogram Methods

Metadynamics, a member fo the "flat histogram" class of advanced sampling algorithms, has been widely used in molecular simulations to drive exploration of states that are separated by high free energy barriers and promote the sampling of full free energy landscapes. A recently proposed variant, paralled bias metadynamics (PBMetaD) promises to aid in exploration of free energy landscape s along multiple important collective variables by exchanging the n-dimensional free energy landscape required by standard methods for n one-dimensional marginal free energy landscapes. In this study, we systematically examine how parallel biasing affects convergence of free energy landscapes along each variable relative to standard methods, and the effectiveness of the parallel biasing strategy for addressing common bottlenecks in the use of advanced sampling to calculate free energies.   

Superfluidity and dimensional cross-over in Quasi-1D systems

1D systems cannot attain long-range order (LRO) but have a wide range of other benefits. One method to cure the missing LRO is to construct an infinite array of weakly coupled 1D systems.
We consider a 3D array of one-dimensional repulsive bosons. If the bosons are hard-core they can model the electron-pairs in e.g. a quasi-1D USC such as the Bechgaard and Fabre salts.
Static Mean-Field (SMF) combined with Density Matrix Renormalization Group (DMRG) reduces the full 3D model to a self-consistently treated 1D one, enabling calculation of ground and thermal equilibrium states. This approach is motivated by the low cost of such an implementation and further allows the simulation of real-time/frequency dynamics.
This model exhibits a phase transition from a 3D superfluid (SF) to a 1D Mott insulator (MI) that forms the basis of the more complex behavior in the USCs. Interestingly, the order parameters indicating the different phases suggest a mix between first- and second-order transitions.

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