A path to calculate emergent properties from first principles in condensed matter

A major theme in physics is that at different energy and length scales, the relevant physical degrees of freedom and equations of motion change. There are special scales where we have very accurate models. One of these scales is at the level of nuclei and electrons, behaving according to quantum mechanics and interacting through electrodynamics. Much of our everyday experience, from metals, insulators and superconductors to living beings can be described as a low-energy limit of this fundamental description, which is often referred to as “first principles.” However, the equations of quantum mechanics for many particles are very difficult to solve, with the general case scaling exponentially in the number of particles. 

In recent years, an understanding has emerged that the low-energy solutions we care about are in some ways simpler than one might expect. Similar to image compression algorithms, these techniques use clever formulations of the problem to reduce the huge amount of data in a naiive representation of the many-body wave function into something more manageable. A collaboration of over 20 research groups have come together to test their techniques against each other for realistic Hamiltonians. With agreement between multiple techniques at an unprecedented level, a new benchmark has been created that can be applied to future quantum algorithms, including quantum computers. 

With the state of the art in calculation of many-body quantum physics being pushed forward, the question emerges—what do we do with these results? We are interested in understanding the effective lower energy physics that emerges from these calculations. I’ll present the current status of a research program that uses data and machine-learning tools from these accurate calculations to derive effective low-energy physics.