Quantum Monte Carlo methods beyond the fixed-node approximation: excitonic effects and hydrogen compounds

NONTECHNICAL SUMMARY

This award supports research and education aimed to make significant advances in simulation and computational approaches for studies of atomic and electronic structures of materials. Understanding, design, and prediction of new types of materials involve solving the equations that describe fundamental quantum mechanical laws for complex, many-particle systems at the level of quantum mechanics.

Such solutions are exceptionally difficult to obtain due to major mathematical, algorithmic and computational challenges as well as due to exceedingly high accuracy required for real world applications. In addition, research on new materials often involves very intricate interplays of quantum phenomena that provide unexpected opportunities to discover materials and new functionalities for information processing, optical, magnetic and host of other applications. This may lead to the discovery of new quantum states of electrons that exist in materials.

The proposed research ideas build upon previous developments of methods known as quantum Monte Carlo, that are particularly promising in overcoming many of the fundamental challenges involved. This successful strategy combines analytical insights, statistical sampling techniques and the power of parallel architecture computing machines into unique and powerful tools that enable us to attack areas of quantum research that were unthinkable even a few years ago.

Key developments involve new algorithms that significantly increase robustness and accuracy of calculating crucial characteristics of materials using a more powerful mathematical framework and more efficient algorithmic constructions. These developments will be applied to two intensely studied groups of materials: i) hydrogen compounds, which are putatively claimed to be new superconductors that would work close to room temperatures; ii) to compounds that exhibit strong quantum phenomena that are essential for optical applications as well as for occurrence of new quantum states of matter.

Proposed projects will provide exciting research, education, and training opportunities for students in quantum physics, computational and simulation techniques, all of which are crucial for technological advances in general and for the next generation workforce. These research and education activities offer a stimulating environment for aspiring young scientists from the growing body of NCSU students, the largest in North Carolina, that includes many students from rural and disadvantaged communities.

Acquired skills in analytical, computational, and modelling techniques are in high demand on job markets throughout academia, national laboratories, and a variety of industries. Preparation to take advantage of such opportunities leads to attractive, highly paid, and intellectually rewarding career paths for future STEM workforce.

TECHNICAL SUMMARY

This award supports research and education aimed to make significant advances in simulation and computational approaches for studies of atomic and electronic structures of materials. Electronic structure quantum Monte Carlo (QMC) methods are routinely used to calculate fundamental gaps, cohesion energies, electronic densities, and other properties by solving the stationary Schroedinger equation with high accuracy explicitly using correlated many-body wave functions.

In this project the PI will expand the ability of QMC many-body wave function methods to describe excitons and excitonic related phenomena in systems with significant electron correlations. For this purpose, pair orbital-based wave functions combined with recent developments that involve two-component spinors will be explored to capture strong correlations in systems that involve magnetic, optical, and collective electronic states.

In particular, this form enables the description of exciton condensates in a variety of materials. The next area of interest involves the application of QMC methods to binary hydride compounds involving a heavier element such as sulfur or yttrium that are putatively claimed to exhibit near-room temperature superconductivity particularly at high pressures.

However, due to experimental challenges the existing data is very limited and our understanding of these materials and phenomena is very far from being settled. The plans involve applications of QMC methods to elucidate atomic and electronic structures, equations of state, and the role of proton zero-point motion and anharmonic effects in these compounds.

At the fundamental level, recent developments for spin-dependent interactions enable smooth variation between fixed-node and fixed-phase versions of QMC. This opens new possibilities to increase variational freedom as well as to reach beyond the current fixed node/phase accuracy limit. The intention is to explore directions that have potential to decrease the commonly encountered fixed-node/phase bias by almost an order of magnitude, opening new avenues for insights into electron-electron correlations and intricate quantum phenomena.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.