CAREER: Quantum anomalies and collective dynamics in symmetry-protected topological phases

University Of Chicago, Chicago IL

Investigators

Abstract

NON-TECHNICAL SUMMARY This CAREER award supports theoretical research that explores exotic quantum mechanical phases of condensed matter, called topological phases, which interact strongly or arise only in the presence of strong electron interactions. The recent discovery of a new state of matter, called the topological insulator, has created great excitement and led to a number of revolutionary developments in condensed matter physics. One of the key features of topological insulators is related to their peculiar transport properties. Usual transport phenomena of electrons (the flow of an electric current) in solids are accompanied with dissipation (Joule heating). Topological states of matter, on the other hand, can support dissipation-free quantum transport through their boundaries while remaining insulating in the bulk. Such quantum transport phenomena of topological origin are promising candidates for electronics and spintronics with low energy cost. Excitations in topological media have also been expected to provide a promising platform for quantum computation that could outperform its classical counterpart by orders of magnitude in terms of computational speed. While non-interacting and disorder-free topological insulators are reasonably well understood, an important next challenge is to understand topological phases of matter that are strongly interacting or that arise only in the presence of strong electron interactions. This is the research theme that is pursued in this project. Electrons in solids can interact with each other strongly through the Coulomb repulsion, and this strong interaction can sometimes lead to exotic, unexpected forms of matter. By developing new theoretical approaches, the PI will search for novel, fully interacting phases of matter that may be characterized by new topological phenomena. The research activities in this project are interdisciplinary in nature and designed to stimulate interactions between condensed matter theory and other fields of academia, such as high-energy physics, computational physics, mathematics, and materials science. Success in these projects will impact many areas of theoretical physics, and may further connect to concrete numerical simulations and to experiments in condensed matter systems. Students and young researchers from various backgrounds, including condensed matter, materials science, high-energy physics, and mathematics will be integrated into the research activities. They will be trained as a new generation of researchers who will be able to work across and between disciplines in the future. In particular, the PI will organize workshops and summer schools for young scientists from the U.S. and Japan on the topic of topological phenomena. TECHNICAL SUMMARY This CAREER award supports theoretical research that explores topological phases of matter, which are strongly interacting or which arise only in the presence of strong electron interactions. By developing new theoretical approaches, the PI will search for novel, fully interacting topological phases of matter that may be characterized by new topological phenomena. A line of attack taken in this project is to use quantum anomalies, i.e. breakdowns of symmetries by quantum effects, to describe and diagnose interacting topological phases, possibly protected by some symmetry. More specifically, this project aims to: 1) Generalize Laughlin's thought experiment, one of the most powerful theoretical tools, which establishes the extreme robustness of the quantum Hall effect against disorder and interactions, in the way it is applicable to a wider range of topological phases, such as topological phases protected by symmetries and topological phases that lack particle number conservation. 2) Use quantum anomalies to construct effective actions and to develop hydrodynamic effective field theory descriptions of collective dynamics of interacting topological insulators and topological superconductors. 3) Establish a connection between anomalous commutation relations obeyed by electron position operators (the coordinate non-commutativity) that arise in topological insulators and collective dynamics of interacting topological insulators. The research activities in this project are interdisciplinary in nature and designed to stimulate interactions between condensed matter theory and other fields of academia, such as high-energy physics, computational physics, mathematics, and materials science. Success in these projects will impact many areas of theoretical physics, and may further connect to concrete numerical simulations and to experiments in condensed matter systems. Students and young researchers from various backgrounds, including condensed matter, materials science, high-energy physics, and mathematics will be integrated into the research activities. They will be trained as a new generation of researchers who will be able to work across and between disciplines in the future. In particular, the PI will organize workshops and summer schools for young scientists from the U.S. and Japan on the topic of topological phenomena.