Séminaire du LPTMS : Hosho Katsura (Tokyo University)

Frustration-free systems refer to a class of exactly solvable quantum many-body systems for which the ground state is obtained as a simultaneous ground state of all local Hamiltonians. They have a variety of applications in condensed matter physics and quantum information, with notable examples including the Affleck-Kennedy-Lieb-Tasaki model and Kitaev’s toric code. A slightly more general concept called the local divergence condition, often discussed in the context of classical stochastic processes, has recently found use in constructing special eigenstates of non-integrable models called quantum many-body scar (QMBS) states. In this talk, I will provide an overview of these technical concepts and then present our recent results. In particular, I will argue that Witten’s conjugation, originally introduced in supersymmetric quantum mechanics, is useful for constructing a family of frustration-free systems based on simple models such as the classical Ising model. If time permits, I will also discuss how to construct QMBS states systematically.