**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.

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.

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.

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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.

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.

In this article, the authors present a technique using variational Monte Carlo to solve for excited states of electronic systems. This technique is based on enforcing orthogonality to lower energy states, which results in a simple variational principle for the excited states.

We develop a continuum dislocation description of twist and stretch moiré superlattices in two-dimensional material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moiré structure.

The parameter derivative of the expectation value of the energy, $\partial E/\partial p$, is a key ingredient in variational quantum Monte Carlo (VMC) wave function optimization methods. In some cases, a naive estimate of this derivative suffers from an infinite variance which inhibits the efficiency of optimization methods that rely on a stable estimate of the derivative.

*#### Hydrogen DFT and QMC data

DFT and QMC data for hydrogen

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-SC-0020177.

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