EAPSI: Investigating the Stability of Particles in Topological Phases of Matter

Cha Matthew, San Diego CA

Investigators

Abstract

A fundamental challenge in science is to characterize states of matter. A phase of matter is a family of states of matter which have very uniform physical properties. Common phases include liquid, gas and solid, which are distinguished by varying temperature. In the 1980?s, scientist discovered new phases of matter in two dimensional electron gas structures, namely fractional quantum hall states. These states possessed particles with interesting statistical behavior, called anyons. In particular, an exchange of two anyons resulted in a multiplication of the state by a complex phase. These new states of matter belong to topologically ordered phases. This project investigates the conjecture that the structure of anyons is stable within a topological phase. This research will be conducted in collaboration with Dr. Yasuyuki Kawahigashi, professor in the Department of Mathematical Science at the University of Tokyo. Dr. Kawahigashi is an expert in the theory of operator algebras and their applications to mathematical physics. The collaboration allows us to further explore the operator algebraic perspective of topological phases and pursue rigorous results in the subject. This research will advance efforts to realize universal quantum computing. We begin by studying exactly solvable Hamiltonian lattice models, in the thermodynamic limit, for which the anyon structure is completely known. These models include Kitaev?s surface codes and Levin and Wen?s string-net models. Each anyon is related to a superselection sector of the algebra of observables. Analysis of the superselection sectors allows one to recover the complete anyon structure, including particle fusion and braiding. Under physically allowable perturbations, we will study the stability of the superselection sectors and particle fusion and braiding. The stability of anyons is the premise of a major program in fault-tolerant quantum computation, namely topological quantum computation. The results of this project form the basis for the continued search for a universal quantum computer through topologically ordered states. This NSF EAPSI award is funded in collaboration with the Japan Society for the Promotion of Science.