Speaker
Description
The nature of topological phases is typically determined by the bulk properties of the system. I will show in this talk that this is not always the case.
I will begin by discussing one dimensional charge conserving superconductors. When open boundary conditions (OBC) are applied, the bulk superconducting instability determines the topological nature of a phase - Spin-triplet superconductor (STS) exhibits a topological phase which is protected by the Z2 spin flip symmetry, with two zero energy Majorana modes (ZEM) at each edge resulting in four fold topological degeneracy of the ground states with exponentially localized fractional spin Sz=+/-1/4 at each edge, while the spin-singlet superconductors (SSS) are topologically trivial with a unique ground state.
I shall show however that more generally the topological nature of a phase depends not only on the bulk superconducting instability, but rather on the interplay between the bulk and the boundary. In particular I will show using Bethe Ansatz and bosonization that SSS can exhibit topological phase stabilized by a topological boundary fixed point when suitable twisted OBC are applied. I will show that a rich phase diagram emerges around the topological boundary fixed point exhibiting several regimes - topological and multiple mid-gap regimes.
In the second part of my talk I will consider dynamical boundary conditions induced by coupling each edge to a Kondo impurity. This allows us to study the Kondo effect in the presence of strong correlations among electrons. I will show that depending on the relative strength of the Kondo coupling and the bulk interaction three regimes will emerge: the Renormalized Kondo regime, the unscreened local moment regime and the YSR (Shiba) regime where the impurity is locally screened by a bound state. The latter exists only in a narrow parameter regime, in contrast to the case of BCS supercondactors where it dominates.
The full phase diagram of the system with two Kondo impurities, one at each edge, exhibits an emergent boundary supersymmetry (SUSY). If time permits I will briefly comment on the similarity of the boundary phase structure of XXZ spin chains and superconductors discussed above and show some DMRG results to compare with.
