A tensor network perspective on anomalies in topological phases of matter

01 October 2018 → 30 September 2022
Research Foundation - Flanders (FWO)
Research disciplines
  • Natural sciences
    • Classical physics
    • Elementary particle and high energy physics
    • Other physical sciences
Project description

Matter can exist in many phases e.g. ice, water and water vapor. The transition between different states (a phase transition) is a remarkable example of emergence and cooperative behavior. When the temperature of the substance decreases, quantum fluctuations take the upper hand and new and unexpected phenomena arise. Such quantum phases were well described before the 1980's by the breaking of certain symmetries, but since then new exotic phases have been discovered that cannot be understood in this way. These phases are called topological phases and their bulk properties are very different from their properties at the edge of the sample. Symmetry plays an important role in their classification and a symmetry that is violated at the quantum level is called an anomaly. Anomalies were only recently discovered to be present in these new topological phases and their investigation provides new ways of classifying topological phases. Quantum entanglement is key in understanding these phases and in the last decade tensor
networks, which naturally encode entanglement, have been very successful in understanding these phases both theoretically and numerically. This proposal aims at a better understanding of these phases from the new perspective of anomalies using tensor networks and the development of new and efficient numerical algorithms to probe this highly fascinating new quantum order for which the 2016 Nobel Prize of physics was awarded.