Topology and edge modes in quantum critical chains

Ruben Verresen, Nick G. Jones, Frank Pollmann

Published 2017-09-11Version 1

We demonstrate that quantum critical points between symmetry protected topological phases in one dimension can display exponentially localized edges modes that are protected by a topological invariant. Unlike previous work on edge modes in gapless chains, this is possible even if there are no additional gapped degrees of freedom. We present an intuitive picture for the existence of these edge modes in the case of non-interacting spinless fermions with time reversal symmetry (BDI class of the ten-fold way), which owe their stability to a topological invariant counting zeros and poles of an associated complex function. This invariant can prevent two models described by the same conformal field theory (CFT) from being smoothly connected, leading to a full classification of critical phases in the non-interacting BDI class. Moreover, the central charge of any CFT in this class is determined by the difference in the number of edge modes between the two sides of the transition. Numerical simulations show that the topological edge modes in critical chains can be stable in the presence of interactions and disorder.