Periodic Reporting for period 2 - PARATOP (New paradigms for correlated quantum matter:Hierarchical topology, Kondo topological metals, and deep learning)
Reporting period: 2019-07-01 to 2020-12-31
In PARATOP we study theoretically materials with qualitatively new behaviors. One of the main new directions are so-called higher order topological insulators, which are three-dimensional crystals that are insulating in the bulk, on the surface, but not on the hinges. Rather, on the crystal hinges we find one-dimensional conducting channels. These channels have the special property that current running through them is dissipationless, that means no power ist lost when the current flows. Such channels may be useful in future ultra-low-power electronics. Aside from predicting new materials with these intriguing properties, develop numerical methods to study the hardest problems of crystals with many strongly interacting electrons. To be able to compute their properties with unprecedented precision, and to predict quantum phase diagrams, we employ neural networks. The neural network represents the quantum mechanical state of the system.
For the numerical investigation of strongly interacting phases of matter, we have mostly focused on code development and benchmarking of the method of neural network quantum states. In that way, one of the PARATOP team members, Kenny Choo, contributed to NetKet, the most prevalent software package in this filed. The results are very promising. We tested the new method on 1D systems, and on the 2D J1-J2 Heisenberg model on the square lattice, which is a iconic model of frustrated magnetism. We found that ground state energy and low-lying excitation energies with new records in numerical precision. More broadly, we studied various applications of machine learning technology to condensed matter physics.
On the forefront of neural network quantum states, we are ready to take the next step and explore systems which have not been studied with comparably powerful methods before, because of computational limitations. In particular, we want to look at 3D frustrated spin systems, for which very few numerically unbiased results exist.
Aside from these two major directions, we will continue to improve our understanding of topological matter in various respects, and improve our code package Wannier Berri.