Geometry and topology have been a fascination in physics since the start of the 20th century. A leading example is Einstein's geometrical theory of gravity. At the beginning of the 1970s, topological ideas entered areas of condensed matter physics. These advances were driven by new seminal ideas resolving a serious contradiction between experiment and the standard interpretation of a rigorous mathematical theorem which led to the study of new exotic topological phases of matter. Topological defect driven phase transitions in thin, two dimensional films of superfluids, superconductors and crystals have provided great insight into the mechanism governing these topological phases present in those physical systems. Moreover, many of these topological properties remain 'protected' against disorder and topological distortion perturbations. An example of possible applications of such robustness to perturbations is in the search for encoding information in quantum computers, potentially providing the platform for fault-tolerant quantum computations.

In the past four decades, the discovery of topological phases engendered great interest in condensed matter physics. It also attracted the attention of researchers working on quantum information, quantum materials and simulations, high energy physics and string theory. This unique volume contains articles written by some of the most prominent names in the field, including Nobel Laureate John Michael Kosterlitz and Professor Jorge V José. They originate from talks and discussions by leading experts at a recent workshop. They review previous works as well as addressing contemporary developments in the most pressing and important issues on various aspects of topological phases and topological phase transitions.

Contents:PrefaceTopological Defects and Phase Transitions (J M Kosterlitz)Geometry of Flux Attachment in the Fractional Quantum Hall Effect States (F D M Haldane)The Attraction Between Antiferromagnetic Quantum Vortices as Origin of Superconductivity in Cuprates (P A Marchetti)Some Topological Phases for Sound (B Zhang)Influences of Geometry and Topology in Nuclei (M Freer)The “Glass Transition” as a Topological Defect Driven Transition in a Distribution of Crystals and a Prediction of a Universal Viscosity Collapse (Z Nussinov, N B Weingartner and F S Nogueira)Surface Ferromagnetism in a Topological Crystalline Insulator (S Reja, H A Fertig, S Zhang and L Brey)Majorana Quasiparticles in Ultracold One-Dimensional Gases (F Iemini, L Mazza, L Fallani, P Zoller, R Fazio and M Dalmonte)Bose Metal as a Disruption of the Berezinskii–Kosterlitz–Thouless Transition in 2D Superconductors (P W Phillips)Topological Superfluidity with Repulsive Fermionic Atoms (G Ortiz, L Isaev, A Kaufman and A M Rey)Clean and Dirty Bosons in 1D Lattices (T Giamarchi)Realizing Quantum Materials with Helium: Helium Films at Ultralow Temperatures, from Strongly Correlated Atomically Layered Films to Topological Superfluidity (J Saunders)Topological Gauge Theory of the Superconductor-Insulator Transition (M C Diamantini, C A Trugenberger and V M Vinokur)BKT Stability Against Disorder, External Magnetic Fields, Classical and Quantum Fluctuations and Quasi-Particle Tunneling Dissipation (J V José)Superfluidity, Phase Transitions, and Topology (J Reppy)Topological Phenomena in the Moiré Pattern of Van der Waals Heterostructures (W Yao)Heterogeneous Interfaces for Teasing Out the Physics of Embedded Surface States (A Hebard)Emergent Particle-Hole Symmetry in Spinful Bosonic Quantum Hall Systems (N Regnault)Dynamical Signatures of Quantum Spin Liquids (F Pollmann)Getting the Jump in the Kosterlitz–Thouless Transition (C Lobb)Phase Transitions: From Josephson Junction Arrays to Flowing Granular Matter (S Teitel)Topological Phase Transitions in Photonic Lattices (Y Chong)Instabilities and Solitary Waves of Light and Atoms in Photonic Crystal Fibres (M Gunn)Spin Topology Architectures in Low Dimensional Magnets (C Panagopoulos)Realizing and Manipulating Topological Metals and their Exotic Properties (Z Wang)Tuning Magnetism and Topology in Topological Insulators with Broken Time Reversal Symmetry (Y Wang)Anomalous Collective Modes in Topological Matter (J Song)
Readership: Graduate students and researchers in condensed matter and theoretical physics.