# Anomalous phase separation dynamics in a correlated electron system: machine-learning enabled large-scale kinetic Monte Carlo simulations

arXiv: https://arxiv.org/abs/2105.13304 · HTML: https://mlsanity.com/paper/2105.13304/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 85 references that are in the map.
- First posted on arXiv 27 May 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [Machine learning dynamics of phase separation in correlated electron magnets](https://mlsanity.com/paper/2006.04205/) (2020)
- [Machine learning electron correlation in a disordered medium](https://mlsanity.com/paper/1810.02323/) (2018)
- [Arrested phase separation in double-exchange models: machine-learning enabled large-scale simulation](https://mlsanity.com/paper/2105.08221/) (2021)

## Built on by (most cited first, 18 of 18)

- [Machine learning nonequilibrium electron forces for adiabatic spin dynamics](https://mlsanity.com/paper/2112.12124/) (2021)
- [Machine learning for phase ordering dynamics of charge density waves](https://mlsanity.com/paper/2303.03493/) (2023)
- [Machine learning predictions for local electronic properties of disordered correlated electron systems](https://mlsanity.com/paper/2204.05967/) (2022)
- [Coarsening of chiral domains in itinerant electron magnets: A machine learning force field approach](https://mlsanity.com/paper/2403.11705/) (2024)
- [Kinetics of orbital ordering in cooperative Jahn-Teller models: Machine-learning enabled large-scale simulations](https://mlsanity.com/paper/2405.14776/) (2024)
- [Machine learning force-field model for kinetic Monte Carlo simulations of itinerant Ising magnets](https://mlsanity.com/paper/2411.19780/) (2024)
- [Machine-learning force-field models for dynamical simulations of metallic magnets](https://mlsanity.com/paper/2602.18213/) (2026)
- [Equivariant Neural Networks for Force-Field Models of Lattice Systems](https://mlsanity.com/paper/2601.04104/) (2026)
- [Machine learning for structure-property relationships: Scalability and limitations](https://mlsanity.com/paper/2304.05502/) (2023)
- [Machine learning force-field models for metallic spin glass](https://mlsanity.com/paper/2311.16964/) (2023)
- [Echo State network for coarsening dynamics of charge density waves](https://mlsanity.com/paper/2412.11982/) (2024)
- [Machine learning nonequilibrium phase transitions in charge-density wave insulators](https://mlsanity.com/paper/2601.07583/) (2026)
- [Graph neural network force fields for adiabatic dynamics of lattice Hamiltonians](https://mlsanity.com/paper/2603.02039/) (2026)
- [Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systems](https://mlsanity.com/paper/2604.11513/) (2026)
- [Machine learning approach for vibronically renormalized electronic band structures](https://mlsanity.com/paper/2409.01523/) (2024)
- [Enhanced coarsening of charge density waves induced by electron correlation: Machine-learning enabled large-scale dynamical simulations](https://mlsanity.com/paper/2412.21072/) (2024)
- [Learning Degenerate Manifolds of Frustrated Magnets with Boltzmann Machines](https://mlsanity.com/paper/2511.19879/) (2025)
- [Graph Neural Network Force Fields for Spin Dynamics in Metallic Magnets](https://mlsanity.com/paper/2607.28537/) (2026)

## Abstract (arXiv)

Phase separation plays a central role in the emergence of novel functionalities of correlated electron materials. The structure of the mixed-phase states depends strongly on the nonequilibrium phase-separation dynamics, which has so far yet to be systematically investigated, especially on the theoretical side. With the aid of modern machine learning methods, we demonstrate the first-ever large-scale kinetic Monte Carlo simulations of the phase separation process for the Falicov-Kimball model, which is one of the canonical strongly correlated electron systems. We uncover an unusual phase-separation scenario where domain coarsening occurs simultaneously at two different scales: the growth of checkerboard clusters at smaller length scales and the expansion of super-clusters, which are aggregates of the checkerboard clusters of the same sign, at a larger scale. We show that the emergence of super-clusters is due to a hidden dynamical breaking of the sublattice symmetry. Arrested growth of the checkerboard patterns and of the super-clusters is shown to result from a correlation-induced self-trapping mechanism. Glassy behaviors similar to the one reported in this work could be generic for other correlated electron systems.