TY - JOUR
T1 - Topology and Edge Modes in Quantum Critical Chains
AU - Verresen, Ruben
AU - Jones, Nick G.
AU - Pollmann, Frank
PY - 2018/2/2
Y1 - 2018/2/2
N2 - We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry-protected topological phases. This is possible even without gapped degrees of freedom in the bulk - in contrast to recent work on edge modes in gapless chains. We present an intuitive picture for the existence of these edge modes in the case of noninteracting spinless fermions with time-reversal symmetry (BDI class of the tenfold way). The stability of this phenomenon relies on a topological invariant defined in terms of a complex function, counting its zeros and poles inside the unit circle. This invariant can prevent two models described by the same conformal field theory (CFT) from being smoothly connected. A full classification of critical phases in the noninteracting BDI class is obtained: Each phase is labeled by the central charge of the CFT, c-12N, and the topological invariant, ω-Z. Moreover, c is determined by the difference in the number of edge modes between the phases neighboring the transition. Numerical simulations show that the topological edge modes of critical chains can be stable in the presence of interactions and disorder.
AB - We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry-protected topological phases. This is possible even without gapped degrees of freedom in the bulk - in contrast to recent work on edge modes in gapless chains. We present an intuitive picture for the existence of these edge modes in the case of noninteracting spinless fermions with time-reversal symmetry (BDI class of the tenfold way). The stability of this phenomenon relies on a topological invariant defined in terms of a complex function, counting its zeros and poles inside the unit circle. This invariant can prevent two models described by the same conformal field theory (CFT) from being smoothly connected. A full classification of critical phases in the noninteracting BDI class is obtained: Each phase is labeled by the central charge of the CFT, c-12N, and the topological invariant, ω-Z. Moreover, c is determined by the difference in the number of edge modes between the phases neighboring the transition. Numerical simulations show that the topological edge modes of critical chains can be stable in the presence of interactions and disorder.
UR - http://www.scopus.com/inward/record.url?scp=85041282197&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.120.057001
DO - 10.1103/PhysRevLett.120.057001
M3 - Article (Academic Journal)
C2 - 29481177
AN - SCOPUS:85041282197
VL - 120
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 5
M1 - 057001
ER -