### Topology and Quantum Criticality: their interplay in one dimension

Mathematical Physics Seminar

24th November 2017, 2:00 pm – 3:00 pm

Howard House, 4th Floor Seminar Room

The ground states of gapped Hamiltonians can form 'symmetry-protected topological phases', characterized by gapless edge modes. In this talk, we explore the quantum critical points between such topological phases of matter in one spatial dimension. Two main questions are addressed, namely how universal properties of the critical point are related to the nearby gapped phases, and whether critical points themselves can be topologically non-trivial. The first question leads to a topological lower bound on the central charge. The second question is answered in full for a class of non-interacting fermions (BDI), with the critical phases being classified by a topological invariant. Curiously, this invariant protects exponentially localized edge modes, even though there are no massive degrees of freedom in the bulk.

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