Starts 6 Apr 2016 16:30
Ends 6 Apr 2016 17:30
Central European Time
We study the response of classical impurities in quantum Ising chains.  The Z2 degeneracy they entail renders the existence of two  decoupled Majorana modes at zero energy an exact property of a finite  system at arbitrary values of its bulk parameters. We trace the  evolution of these modes across the transition from the disordered phase  to the ordered one and analyze the concomitant qualitative changes of local  magnetic properties of an isolated impurity. In the disordered phase,  the two ground states differ only close to the impurity. In this phase the  local transverse spin susceptibility follows a Curie law.  The critical  response of a boundary impurity is logarithmically divergent and maps to  the two-channel Kondo problem, while it saturates for critical bulk  impurities, as well as in the ordered phase. The results for the Ising  chain translate to the related problem of a resonant level coupled to a  1d p-wave superconductor or a Peierls chain, whereby the magnetic order is  mapped to topological order.  We find that the topological phase always  exhibits a continuous impurity response to local fields as a result of the  level repulsion of local levels from the boundary  Majorana zero mode. In  contrast, the disordered phase generically features a discontinuous  magnetization or charging response. This difference constitutes a  general thermodynamic fingerprint of topological order in phases with a  bulk gap.