# QMC-HAMM

High accuracy multiscale models from quantum Monte Carlo

The QMC-HAMM project is based on quantum Monte Carlo (QMC) techniques to accurately compute the properties of materials very accurately. Multiscale models are then derived based on these accurate calculations.

# Mission

A major theme of condensed matter and materials physics is the relationship between the microscopic behavior of electrons and nuclei to the emergent low-energy mesoscopic behavior of materials. Elucidating this relationship is a challenge, since the microscopic model requires advanced solution methods for many-body quantum mechanics, and the mesoscopic picture can be rather complicated. In complex materials, standard concepts at the mesoscopic level such as phonons, spins, and electron-like excitations can interact in complex ways which are difficult to access experimentally.

The state of the art in creating mesoscopic models starting from microscopic behavior is based on density functional theory (DFT) calculations. In recent years, modern machine learning techniques have been able to reproduce potential energy surfaces from standard DFT functionals to a very high accuracy; the accuracy potential energy surfaces can be limited by the underlying data. In quantum materials such as twisted bilayer graphene,(pictured above) interactions between electronic excitations can be critical to their behavior. To resolve the above issues, it is necessary to move beyond density functional theory and to base mesoscopic models on more accurate microscopic calculations. In this project, we will use quantum Monte Carlo calculations as a base for high-impact projects which can benefit from the extra accuracy.

# Vision

At each length scale of interest, advanced tools exist. Our collaboration contains experts at each of these length scales. Our goal is to systematically link the microscopic to the mesoscopic by using well-defined data interfaces. The highly accurate, sub-atomic scale quantum Monte Carlo calculations produce data, which is then used to understand the physics at the atomic scale, and so on. Reproducibility and documentation are achieved by using modern scientific computing methods.

# Recent Publications

Quickly discover relevant content by filtering publications.

### Stability and distortion of fcc LaH10 with path-integral molecular dynamics

The synthesis of the high temperature superconductor LaH10 requires pressures in excess of 100 GPa, wherein it adopts a face-centered cubic structure. Upon decompression, this structure undergoes a distortion which still supports superconductivity, but with a much lower critical temperature.

### Accurate tight-binding model for twisted bilayer graphene describes topological flat bands without geometric relaxation

A major hurdle in understanding the phase diagram of twisted bilayer graphene is the roles of lattice relaxation and electronic structure on isolated band flattening near magic twist angles. In this work, the authors develop an accurate local environment tight-binding model fit to tight-binding parameters computed from ab initio density-functional theory calculations across many atomic configurations.

### Phonons of metallic hydrogen with quantum Monte Carlo

We describe a simple scheme to perform phonon calculations with quantum Monte Carlo (QMC) methods and demonstrate it on metallic hydrogen. Because of the energy and length scales of metallic hydrogen and the statistical noise inherent to QMC methods, the conventional manner of calculating force constants is prohibitively expensive.

### An efficient computational framework for charge density estimation in twisted bilayer graphene

Electronic properties such as band structure and Fermi velocity in low-angle twisted bilayer graphene (TBG) are intrinsically dependent on the atomic structure. Rigid rotation between individual graphene layers provides an approximate description of the bilayer symmetry.

### Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: Above and below the upper critical range

Understanding the low-temperature pure state structure of spin glasses remains an open problem in the field of statistical mechanics of disordered systems. Here we study Monte Carlo \emph{dynamics}, performing simulations of the growth of correlations following a quench from infinite temperature to a temperature well below the spin-glass transition temperature $T_c$ for a one-dimensional Ising spin glass model with diluted long-range interactions.

# Data products

Model

Model

#### Hydrogen DFT and QMC data

DFT and QMC data for hydrogen

# Meet the Team

Continuum models

Tight binding

## Lucas K. Wagner

### Professor of Physics

Quantum Monte Carlo, Multiscale quantum models

## Andriy Nevidomskyy

### Professor of Physics

Correlated lattice models

## David M. Ceperley

### Professor of Physics

Quantum Monte Carlo, High pressure hydrogen

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# Acknowledgments

This project is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Computational Materials Sciences program under Award Number DE-SC0020177.

Support of the Materials Research Lab at the University of Illinois is also gratefully acknowledged.