Topology and Quantum Criticality: their interplay in one dimension

Critical points between one-dimensional symmetry-protected topological (SPT) phases are explored. We classify these for non-interacting superconducting spinless fermions with time-reversal symmetry (BDI): the gapless phases are labeled by the central charge (of the conformal field theory) and a topological invariant. The latter invariant protects exponentially localized edge modes, despite there being no gapped degrees of freedom in the bulk. Moreover, the central charge of the critical point obeys a topological lower bound, determined by the nearby gapped phases. We conjecture such a lower bound to hold for all transitions between one-dimensional SPT phases, as supported by analytical and numerical examples.