This award supports theoretical research and education into new phases of matter, called topological phases. As Landau discovered, states of matter such as liquids and crystals can be organized through understanding what symmetry transformations can be performed on a given state that leaves it unchanged. For example, a rotation of 90 degrees around a principle axis of a crystal of common salt, rotates new atoms into positions that were originally occupied by the very same kind of atom, so the crystal appears unchanged. The concept of symmetry also allows magnetic and other states to be organized by similar considerations. In recent years, it has been discovered that ideas from topology, the branch of mathematics concerned with geometric properties that are unchanged by deformations, twisting, and stretching objects, brings insight into new possible phases of matter, called topological phases. Among these are topological insulators that are fundamentally different from ordinary insulators in that while the bulk does not conduct electricity, their surfaces do, as if they belonged to a metal.
This award supports theoretical research that will use topological phenomena like the metallic surface states to develop a systematic theory of topological phases. Quantum entanglement is expected to play a crucial role in this theory which will enable the search, discovery, and design of new topological states. Quantum entanglement refers to the phenomenon whereby states of individual components of a system, eventhough the components may be spatially separated by large distances, cannot be described independently of each other; as a consequence of quantum mechanics, the individual components act in a correlated way.
Topological quantum entanglement leads to possible amazing phenomena, including electric charge that is a fraction of an electron charge, particles that are in a fundamental sense between electrons and photons - the quantum of light, and a more unified understanding of the origin of light and electrons. New topological states may be discovered or designed that can form the foundations for computation that utilizes the manipulation of quantum mechanical states, a topological quantum computer.
This award supports theoretical research and education with the aim of discovering new theoretical concepts and methods to more precisely develop a comprehensive theory of topological phases and symmetry protected topological (SPT) phases. The research has 4 parts: (1) develop a system to label topological /SPT phases; (2) discover a set of physical measurements that can measure and distinguish different topological phases; (3) create a mathematical theory that allows for the classification of all topological phases; (4) develop effective methods to enable the calculation of the phase diagram of a generic system that contains topological/SPT phases.
This research may lead to the discovery of a new class of quantum materials, highly entangled topological materials, which may provide the foundations for a new class of device concepts and electronic and optical devices made possible by exploiting quantum entanglement. The development of the theory may require or stimulate the creation of new mathematics and may lead to fundamental insights into areas extending from quantum computing to elementary particles.
