Using Supersymmetry to study Condensed Matter Systems
ABSTRACT :
Supersymmetry in 3+1 dimensions was introduced as a way to relate bosons and fermions thus generalizing the notion of symmetries. In 0+1 dimensions this algebra simplifies and it becomes supersymmetric quantum mechanics (SUSYQM). Tradition- ally these algebras are realized using fermionic oscillators. In this talk I will introduce another way to formulate SUSYQM systems using the algebras of inverse semigroups. The traditional approach can be seen as a special case in this formulation. Using this algebra we study two condensed matter systems. The first set is a class of integrable many body systems that have Local Integrals of Motion (LIOMs). Such systems have zero transport properties and are seen to be examples of Many Body Localized (MBL) states. We confirm this by computing the out-of-time ordered correlators (OTOCs) in the models. For the second part we see how we can use these new SUSY algebras to relate multiple modes in optical structures.