## Topology and Entanglement in Correlated Quantum Systems (5715)

July 14, 2014 – August 08, 2014

#### Location

Dresden, Germany

Organizers

Frank Pollmann, Max-Planck-Institut

Erez Berg, Weizmann Institute

Nigel Cooper, Cambridge University

Xiao-Gang Wen, Perimeter Institute

Overview

It is one of the goals of condensed matter physics to find organizing principles for understanding the different phases of matter which occur in nature. A notable milestone in this direction was the introduction of the Landau-Ginzburg theory, which analyzes states of matter according to their spontaneously broken symmetries, characterized by local order parameters. This theory was for a long time believed to provide an almost complete description of phases of matter (with a few exceptions, such as the “Fermi liquid” phase formed by electrons in a metal). In recent years it has been discovered that topology can play a crucial role in understanding certain phases of matter. In these phases, the system does not break any symmetries, yet some hidden form of order is present. The fractional quantum Hall effect is the best known example for such a phase. One of its characterizing properties is the existence of emergent excitations having anyonic statistics. While the elementary constituents of the systems are either bosons or fermions, the composite excitations of the system behave in a way that resembles neither. Winding one anyon around another results in a phase different from 0 or π (abelian anyons), or in a unitary transformation acting on the ground state manifold (non-abelian anyons). It is clear that such fascinating behavior could not exist if the constituent particles were independent of one another. Therefore, inter-particle interactions are essential; a ground state whose excitations are anyonic is necessarily a state in which the underlying particles (e.g. electrons) are strongly correlated with each other. The emergence of excitations with exotic statistics is a manifestation of a hidden form of order, generally known as topological order, which has been a source of much interest and excitement recently. While the occurrence of topological phases in systems of non-interacting fermions (such topological insulators) is by now rather well understood, the general understanding of such phases in the presence of strong interactions is, to a large extent, still at its infancy. The interest in this topic, in our view, is twofold. First, topologically ordered phases go beyond the traditional “Landau paradigm”, and therefore these phases represent a fundamentally new class of phenomena, which are now only beginning to be explored. Second, the topological nature of these systems may make them attractive as ingredients for quantum information processing applications. This is because the quantum information stored in the state of the system tends to be well protected from coupling to the environment, making it immune to decoherence. The proposed program is designed to attract physicists from a broad range of disciplines, including theoretical and experimental condensed matter physics, atomic physics, quantum information theory, and computational physics. It will include an intensive one-week conference and a three-week seminar program. The program will provide plenty of time for people to interact with each other and discuss open problems in the field. In order to make the conference more stimulating and fertilizing, talks about emerging questions and new, unpublished results will be encouraged.