Title: Supersymmetry on the lattice: Geometry, flat bands, and topology

Speaker: Dr. Krishanu Roy Chowdhury, SINP, Kolkata

Gmeet Link: https://meet.google.com/tmf-qjgx-dso

Abstract: Supersymmetry (SUSY) posits an equivalence between two fundamental degrees of freedom: fermions and bosons. Using this, a variety of phonon and magnon models can be identified which have topologically nontrivial free fermion models as superpartners. At the single-particle level, the bosonic and the fermionic models that are generated by SUSY are isospectral except for zero modes that potentially manifest as flat bands on various lattices. Relating it to a topological index, the SUSY theory enables a five-fold classification of band touching involving flat bands. Extending further to real fermionic and bosonic degrees of freedom, we can systematically construct topological mechanical systems as superpartners of Majorana models using our SUSY approach. Such a construction naturally defines hitherto unexplored topological invariants for bosonic (mechanical) systems, such as bosonic Wilson loop operators that are formulated in terms of SUSY-related fermionic Berry curvature. In summary, our SUSY construction is useful to identify topological bosonic models whose fermionic partner realizes a symmetry-protected topological phase.