TSU COLLOQUIUM

Colloquium

Title: Supersymmetry on the Lattice: Geometry, Flat Bands, and Topology

Speaker: Dr. Krishanu Roychowdhury

Affiliation: Max Planck Institute for the Physics of Complex Systems, Dresden, Germany

Date and Time: 9th January 2023 (Monday) at 02:30 PM (Tea: 02:15 PM)

Place: AMRL Conference Hall

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. The existence of such flat bands is intricately related to a nonzero Witten index of the SUSY theory that admits a five-fold classification.

Extending this SUSY to real degrees of freedom, we can systematically construct topological mechanical systems as superpartners of Majorana models. 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 represents some symmetry-protected topological phase.