A Quantum Universe in a Crystal: Symmetry and Topology across the Correlation Spectrum

Coordinators: Jennifer Cano, Taylor Hughes, Qimiao Si, and Senthil Todadri

Topology is emerging as a key player in several different and seemingly disparate directions. The combination of symmetry and topology has revolutionized band theory, giving rise to a host of new topological phases in crystalline materials. Recent highlights include topological semimetals with Weyl and Dirac fermions and “higher-order” topological insulators.At the same time, new platforms for topological phases have been discovered in strongly correlated settings, including systems with Kondo-driven Weyl fermions and materials that contain geometry-induced flat bands. Topology has also provided useful non-perturbative insights into the difficult problem of understanding gapless states of matter. Recently, the three big topics of topology, symmetry, and interactions have come to a head in heavy fermion systems and moire materials.

These developments motivate a concerted effort to confront the interplay between topology, symmetry, and interactions. The goal of this program is to use topology to build connections between the vast universe of quantum phases that appear in crystalline materials, from the weak to the strong correlation regime. The program will shed light on topics such as the development of non-Lorentz invariant field theories to unify crystalline topological phases; the cooperation between symmetry-based concepts developed for topological band theory and strong correlations in creating correlated topological states; and the role of topology to describe novel strongly correlated gapless phases of matter.

The outcome will be a new wave of theoretical approaches that will further solidify a web of interconnected topics related to geometry, topology, symmetry, and correlations in the formation of quantum phases of electronic matter, as well as enhanced interactions between theorists and experimentalists that will undoubtedly be essential to advancing this field.