SEMINAR:Some Applications of the Modern Theory of Polarization..

Speaker: Balázs Hetényi

Title: Some Applications of the Modern Theory of Polarization: Topological Systems and Disorder

Date/Time:1 June  2022 / 13:40 - 14:30

Zoom link: https://sabanciuniv.zoom.us/j/96948705087?pwd=N3ZxcFp5ZXgzamJObGI5cXNmN0tMdz09

Abstract:The modern theory of polarization casts the polarization of a crystalline system as a geometric phase.  The geometric phase here is of a particular kind, the so called Zak phase, obtained by integrating across the Brillouin zone.   This developmet is already some decades old, but the recent upheaval in topological physical systems has extended the theory.  Topological invariants are often modified “polarizations”.  In this talk I will discuss two problems we studied in this context.  One is the question of basis fuctions to use in bi-partite lattices.  The most common bases used in the literature either contain explicit distance depedence of sublattices, or not.  We study this question in a modified SSH model, which is derived from the Haldane hexagonal model by projecting along one dimension.   We show that the model can be represented by toroidal knots whose winding numbers are related to the polarization.  The second topic is the application of the modern theory of polarization to disordered systems.   We develop a renormalization analysis which uses the machinery of the theory, which we apply to the question of dimensional dependence of criticality in disordered systems.  We compare our results to the famous “gang of four” paper.  In one and three dimensions we reproduce their conclusions.  In two dimensions we can not say this exactly, but most likely we face system size limitations.