A tensor network perspective on the relation between topological and conformal field theory

01 November 2019 → Ongoing
Research Foundation - Flanders (FWO)
Research disciplines
  • Natural sciences
    • Statistical mechanics, structure of matter
    • Algebraic structures in mathematical physics
    • Classical and quantum integrable systems
    • Quantum information, computation and communication
field theory
Project description

Phases of matter are a familiar concept to most, and everyone understands that if you heat up a piece of ice it will turn to liquid water and eventually to steam. It is therefore surprising that it took physicists until well into the 20th century to write down theories to systematically treat these phenomena. It turns out that the concept of phases and phase transitions are intemately linked to the symmetry and symmetry breaking of a system. The phases we encounter in everyday life are driven by thermal fluctuations, but the advent of quantum mechanics brought with it phases that are driven by quantum fluctuations. Initially, it was thought that these phases too admit a classification entirely in terms of symmetry and symmetry breaking, but experimental observation indicated the existence of types of phases that do not fit this framework. New theories were required that rely only on the topology of the system, or put more plainly, whether we put it onto a sphere or a torus. These physics of these systems is entirely independent of distances, and it is therefore said that these theories have zero correlation length. It is then very surprising, that if we look at the boundary between two such theories, we find a theory with infinite correlation length. This phenomenon has been studied extensively in the continuum, but a systematic study on the lattice is lacking. Using tensor networks, which have been tailor made to describe discrete systems, we aim to further probe this fact.